Check out Blades in the Dark -- it has _exactly_ this mechanic! (And is also my favorite RPG system)
Money in BitD is very abstract, and a single coin represents a serious amount of money. And you don't buy stuff with it because you can only take so much stuff with you, and what that is depends on your character. Instead you use it to upgrade your lair or bribe people, I think.
So it's not quite what I was thinking of, although it certainly has some of the elements. Maybe it has shaped how I'm thinking about it now.
I remember how longer ago, I was thinking of a Robin Hood game where character progression depended on how much money you gave to the poor. That way you can still buy stuff for yourself and not level up, or give to the poor and level up.
A game centered around moving money, but not acquiring it, could be very interesting. You could tease out a few interesting scenarios and have meta-progression where helping others can create a network of skills. (i.e. you helped the baker pay her debts, now she will bake bread for you at cost.)
https://bladesinthedark.com/downtime-activities
> A PC can make time for more than two activities, at a cost. Each additional activity from the list costs 1 coin or 1 rep. This reflects the time and resulting resource drain while you’re “off the clock” and not earning from a score. When you complete a new score, you reset and get two “free” activities again.
Spending coin on stress reduction certainly helps. If a player gets a 2-coin reward for a score, I'd hope they stashed one and burned one on something.