Every D&D adventurer is a coin collector.
Every old variety of D&D and similar games posit one game-mechanical goal for characters: collecting coins (and other treasure evaluated in coins).
Coins are a symbol in these games for the characters' trying experiences that explain their personal improvement. We all know that gathering gold does not make one a more skillful fighter or wizard or thief. The coins accumulated represent the achievement of the tasks, and it is carrying out tasks that serves as training in skills. As a symbol for experience, the gold piece has been pretty sufficient, as it's still widely used.
Adventure scenarios contain hidden and protected coins, and other treasures evaluated as coins, which are the inducement to adventure. Players are spurred by the knowledge that coins are out there to take risks with their characters, producing a fun social event with elements of gambling, risk-free vicarious danger, cooperative problem-solving, and role-playing. The game is a treasure hunt with obstacles in the way. And that's fun!
In D&D, then, coins are not really coins. They are vague, shiny rewards, findable units of experience.
If they were actually fully imagined as coins, they would have some of the characteristics of coins. Instead, in practice, they are generic.
The symbolic character of gold pieces in these games has kept the coin as one of their least examined and most generic aspects. For a game aiming at a fantastic-medieval ambience, this seems like several missed opportunities.
Weight and value
If we took the Roman silver (denarius) and late Roman gold (solidus) coins as models, then these were ideally about 4.5 grams each. That makes approximately 1 pound per 100 coins and 10 pounds per 1000 coins for either silver or gold. It's a neat equation for those who are tinkering with encumbrance rules.
There are other possibilities, if a referee wants to create complications. Coins can have varying weight but the same value if they are relatively debased (mixed with less valuable metals), for example. What if the coins in one realm weigh 150% or twice as much, but had the same value, as the coins familiar to the player characters? What if player characters exert a lot of effort to recover coins that turn out to be poor quality products and have less value on the market?
Mints and images
The symbolic nature of coins in D&D reinforces their vague and shiny lack of character.
Historical coins, by contrast with D&D coins, were minted by specialists entrusted with the precious metals by a ruler or government. A team of experts would pour the metal, strike the coin, cut the edges, and clean it up for controlled circulation.
Coins were issued by individual rulers. They showed the face or figure of the specific ruler, usually with a short legend stating the ruler's name ("of King X").
Coins often also showed an ideological image on the reverse: a religious symbol, the representation of a divinity or a temple, or another image legitimizing the ruler who issued the coin. The ruler's image vouched for the value of the coin and the coin attested to the legitimacy of the ruler.
Coins would often be marked with a symbol or abbreviation indicating where they were minted.
A major function of coins was originally to pay soldiers, who received these bits of precious metal embossed with the image of the man who paid them. Soldiers then spent coins at large, gradually monetizing the economy. Coins were also useful as units of exchange in collecting taxes.
New kings would gather old coins and have the material minted into new coins with their faces. Old coins became rarer because of that.
Coins plundered from one country would be melted down and turned into new coins for the conquering state.
Thus coins were marked for a time and a place.
In developing spontaneously emergent game worlds, there is little time to whip up a historical backstory to the setting, and many D&D players have become averse to setting backstories (which do tend to be generic and boring). But without any established background, coins will remain faceless and without character, pure shiny symbols of hurdles overcome and not a part of a setting.
Coins that are merely symbolic, without the characteristics of coins, are practically metagame features intruding into the narrative. Coins without character or setting context are just experience points in symbolic form, as if you had a belt of spell slots or could see the plusses engraved on your magical sword.
Questions for your game
Once you consider that coins are marked by origin, many new questions can arise that may color your game.
When player characters spend money, do the coins indicate from which country they, or their currency, comes?
When they gather coins lost in old dungeons, will markets outside accept the coins stamped by forgotten kings? Will they be more, or less, valuable than current coins? Do they need to be exchanged for new coins (at a loss) to representatives of the state or moneychanging middlemen? Will they need to be melted down by somebody and sold as bullion?
Will trading ancient coins mark the adventurers as grave robbers?
Will government authorities take an interest in the sudden influx of strange coins marked with the faces of ancient or foreign kings?
Will dungeon treasure spent at a village near the dungeon not make the locals fabulously rich, to the point that they move away or retire? Will dungeon treasure spent locally create a boom town and a wave of crime? Won't the influx of coins inspire bandits who prey on adventurers returning from the local dungeon with low hit points and sacks full of jingling gold pieces?
Will local authorities attempt to confiscate illegitimate currency? Won't they claim a huge cut from adventurers plundering sites in domains that they claim as their own?
Can player characters rediscover lost history through the coins they recover? Can the discovery of coins minted under the rule of a long-forgotten Wizard King spur new adventures?
Would a map to the mint of an ancient state prompt a quest? Would a raid on a mint, run by humans or humanoids, not make an ideal adventure in a world in which coins symbolize the advancement of skill?
Would an effort to mint new coins by PCs who create their own freehold spark a war with an adjacent power insisting that its coins are the only valid ones?
If you search for images of "ancient coins" on the internet, what inspiration will you find?
The most familiar type of coin, in the shape of a little flat disk with images on its two sides, originated in the kingdom of Lydia (today, western Turkey) in the seventh century BCE. It caught on from there. The vast Persian Empire, which included Lydia early on, from the sixth century BCE, spread the use of coins far abroad.
But different kinds of tokens of exchange can be used in adventure games.
Loops of metal, cowrie shells, boar tusks, stamped bits of clay, and other units can be traded as tokens of value.
What if the players visit a country where gold or silver are not wanted, but shells or crystals are?
Rationales for XP = GP
A common way to bridge the narrative gap, to rationalize the increase in power that comes from finding gold pieces, is to say that player characters have to spend their treasure to gain XP and to gain a level.
One way is to say you have to spend your GP on training to get the XP. This implies the existence of high-level trainers, who themselves may become a "rare commodity." Maybe the goal of every adventurer is to retire to become a highly-paid trainer of lower-level adventurers in a cosmic experience point pyramid scheme. Soon you can earn whole dungeons worth of treasure without undertaking any danger, but collecting dungeon treasure from the lower-level peons who do the dirty work and pay you for training, so that they can retire and be trainers like you.
Another way is to say you have to spend the GP on fun and debauchery, to make the GP into XP only when it's "useless," and not for equipment or fortifications or the like. Only celebratory, wasteful expense gives XP. Personally, I find this odd as just another violation of story rationale (wasting money, or pleasure, makes a wizard into a better wizard?), but it works for some players.
The idea of giving experience points that accumulate gradually and with excitement until the joyous burst of a level-up reminds me of the video games about Sonic the Hedgehog. The blue critter runs and runs, collecting shiny gold rings. Every so often, the accumulation confers bonus powers. Clearly, the mechanic in this video game and others like it derives from D&D.
But what if we cut out the tokens and went straight to the power-ups?
What if adventurers were primarily seeking not gold, but rare objects or locations that conferred those level ups? Sure, gold is useful, but maybe the level-ups are separate.
I call this found advancement. Instead of discovering little bits of treasure that symbolizes the gradual training experience--which culminates with a sudden growth of power--and burdens us with a need to rationalize the gap between gold accumulation and power, player characters just discover [narrative symbols of] level-ups in the dungeon or wilderness.
What if, instead of collecting coins painstakingly, player characters were instead seeking the lost Shrine of Power? Anybody who enters the Inner Sanctum there gains a level. This may be more climactic than tallying up coins over long periods. It also creates a narrative that matches the momentary experience of a level-up with a momentary event (rather than a gradual accumulation leading to a momentary event).
You can use this method for games with levels, but also in games without levels (as I do in my home rules). It works wonderfully in games with narrative advancement.
Player characters who find the inaccessible Fount of Life and drink from its luminous waters gain a level, a hit die, a point of Constitution or Endurance, or whatever the referee has decided.
If they restore the Sacred Orb to the Temple of Fortuna, they gain a level... or a point of Luck, or Wisdom, or whatever the referee has decided.
The first one to touch the Heart Crystal, deep in the underdark, gains a level... or a new spell, or a magical ability, or whatever the referee has decided.
Players who destroy the Eye of the Lich release its pent-up accumulation of life-force and absorb a level-up, more hit points, or whatever the referee has decided.
Adventurers who reach the remote mountain of the Monastery of Mastery can undergo a test (or deliver an object) that will admit them into a training program, giving them a new level, a new ability, or whatever else the referee has decided.
Instead of populating your adventure settings with mounds and mounds of symbolic coins that have no character and little connection to the setting, you can create setting locations and objects that directly confer the bonuses that incite adventure, and that are intrinsic to the story of the setting.
Your sandbox world can have a bunch of these sites. Hide them in remote spots, under slabs of stone in ruins, behind dragons, in deep caves. If they are easier to find, then they can only confer a full level-up to a certain level; they give a smaller bonus to higher-level characters.
Found advancement doesn't make gold pieces useless. Players need cash for all kinds of things.
Found advancement can help you to put the focus on discovery over loot.
Populate your rumor table with references to lost magic, sites of power, and treasures that confer level-ups.
Experience shows that players are just as eager to push their characters to these kinds of discoveries as they are to impel them to seek treasure in the form of generic gold coins.
This is a way to handle experience points and levels, but it also works well for games with narrative advancement (what people sometimes call "diegetic advancement"). You don't need numbers for this.
Let me know if you try it and how your players respond.