The expectation is that about 80% of XP earned through Adventuring would come from recovered treasure. However, as a GM I dislike the effort it takes to start counting every copper recovered, trying to determine the price off oddball magic items that are sold, etc. What I intend to do instead is only calculate the XP from overcoming monsters, and multiplying this value by 5. This would save me some time, and would avoid the weird effect that taking out rich wimps can lead to more XP than taking out poor tough guys. This would not replace the XP earned from Campaign activities such as running domains and mercantile ventures. Does anyone see a downside from making this simplification?
The fact that you are calling it "overcoming" monsters rather than defeating suggests that you're taking steps to avoid this becoming more encouraging of combat and slog fests. Unfortunately I think it still won't work out exactly the same because treasure can come from other parts of the dungeon, such as traps or hidden rooms.
Another thing to consider: while wealth can be its own reward, there is much less incentive to attempt to acquire wealth more than the minimum necessary to cover expenses. This could lead to players getting into sticky situations where they can't pay their henchmen or other retainers. Maybe this is an interesting dilemma you'd like to encourage.
Overall, death may become a good deal more dangerous, since being less flush with cash means less reserve XP, which defrays the cost of dying. Certainly wealth will get closer to normal amounts at higher levels, but that's also when death is a bit less scary since Restore Life & Limb is affordable.
Personally I like that certain monsters are worth more because of their treasure over their fighting potential. I think it leads to smart play "We don't need to risk our lives on those zombies, I don't think they have any treasure, but those goblins had a magic staff, lets ambush them."
The reason XP is awarded for mostly for GP instead of for combat is to help synchronize player and character mindsets. Most humans would greatly prefer to have money than to get in a fight. Pretty much the only people who say "I wanna fight that really deadly looking guy. I bet it'll be a really tough fight and that's what I'm into!" are shonen anime protagonists. To me, having that as the default mindset for your PCs is way, way stranger than noticing that people who choose their fights carefully tend to get ahead in life faster.
It's also useful for synchronizing player and DM expectations. Whether or not you collected a gold piece is very clear. Whether or not you "Overcame" a monster can be ambiguous. If the party steals the treasure a minotuar was guarding, that's probably overcoming. But what if they trade it for an equivalent treasure? What if they hire a high level wizard to scry the treasure and teleport it directly out of the vault? Do they get XP for the entire dungeon? If your players have different opinions than you do, that could be a source of conflict. If you did GP for XP, the answer would always be very clear to everyone at all times.
The last thing is that really good dungeon design relies on there being things the PCs want, and things the PCs want to avoid. One of the best moments of dungeon-mastery is the first time a PC says "Hey, we left the underwater tunnel because of the skeletons, but I bet it keeps going all the way over here to the south catacombs. If we get some potions of Undead Ignore You, I bet we could completely bypass the Spider Tunnels!" and then everyone cheers because they did NOT want to fight spiders. After all, spiders are dangerous and don't have much treasure. Quintupling their XP value makes fighting the spiders an OK prospect, so there's no need for clever pathfinding. That makes me sad.
The last reason is that the 80% is a guideline. You really shouldn't be counting up every copper. Generally I just look at the Expected Average Values, and then roll whatever is appropriate for that treasure type, and then spread that treasure across the dungeon. If there's 200xp worth of monsters, I pick, say, type C or whatever is worth 1000ish, roll it, put most of it in lairs, and then sprinkle the rest behind hidden doors and stuff.
Hmmm. Maybe I'll still multiply the monster XP x 5, and just let the players think the original XP rules are in play. They don't do audits on the XP awarded anyway.
I think Susan makes excellent points here.
If your game is anything like mine, there will be sessions where the PCs have several fights and have garnered little to no treasure but have to return to civilization to rest and hire more cannon fodder. As a recent personal example, one can adventure/fight a long way into B5 Horror on the Hill without finding any treasure... If they get substantial XP in those instances they'll figure something is off, audits or no audits. In any case, I think transparency with your players about the game's reward mechanics is the best policy.
If you're concerned about rich wimps, you might consider requiring downtime and PCs having to spend coin for martial/divine/mystical training to gain some portion of their XP. Then it's not the mere acquisition of money that allows PCs to level up, but its translation into professional training.
I would definitely argue for not lying to your players about core game mechanics.
Fundamentally, what gives players XP in a game is what that game seeks to reward. If only overcoming monsters gives XP, that's what players will naturally want to do. If finding treasure gives 4x as much XP, players will want to find treasure about 4 times as much as they want to engage with foes.
This is more explicit in other games like Dungeon World: you get XP for failing die rolls (aka trying something you're not an expert at), for fulfilling bonds (ie: roleplaying a relationship between you and another player), for fulfilling your alignment (another roleplaying prompt) and for learning new things about the world. Thus, the game encourages players to develop relationships with each other, to stick to their alignment even when it's not optimal play, to attempt to things even if they're not good at them, and to learn more about the world.
Deciding what grants XP in your game should always be a decision in what kind of play you want to reward and therefore emphasize.