I've played Blades in the Dark, and while you accumulate stress, you roll to get rid of it. I don't think it costs actual money, although they do call it vices. My plan was to really tie it into the excessive accumulation of money in D&D-style games, which is a problem BitD wouldn't have even if it didn't have the stress mechanic.

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.