Oooo this is super interesting! For sure, the city needs to have something that the players don’t have, a reason for them to choose stealing from an urban center instead of living in nature or by themselves. (I would think this is analogous to how the OSR character tends to be an excess of society–the reason they’re adventuring is because they can’t slot into socioeconomic “harmony” with the rest of the world).
Maybe the city has exhausted all the resources outside of its walls, but inside they have vast stores of food and water and so on? And, either the characters have always been outsiders reliant on the resources outside the city, or they’ve been forced out of the city and they’ve lost their access to the city’s resources.
In the latter case, XP/leveling serves as a measure of how well-adjusted a character is to the world outside of the city. A LVL 1 character has just been thrown out of the city walls and left to fend for themselves. A LVL 3 character might be someone who’s reliable and competent enough to survive on their own outside.
Gold for XP might still be a useful measure, but like you said, it can’t be because the party finds gold useful (unless they are still enough a part of society to engage in exchange). Maybe instead, you refer to gold as a measure of society’s output that the party has successfully taken for themselves? Like, stealing a turkey leg is less valuable than stealing a wagon. But maybe a luxury wagon is not super useful for the players even if it’s socially valuable apropos the city–why would they steal it? You might have to work on a value system based on what’s useful/valuable for the characters, or rely on GM fiat to decide how valuable/risky a stolen item is.
This is a super interesting concept and I’m excited to see where you go with it! Maybe you could set up a game jam of various scenarios where the players exist outside of the city, to explore the concept thematically and logistically before committing to a system?