I dislike wealth levels as a mechanic. In games where accumulating wealth is a motive for play e.g. playing tomb robbers, pirates, smugglers, mercenaries, or treasure hunters, wealth levels are an odd abstraction "you find a chest worth 2 wealth levels" just doesn't resonate or sound cool when compared to "the chest is filled with gold doubloons. There must be at least a thousand coins there."
Even if the game is not about accumulating wealth, wealth levels come across like currency where the smallest coin is $1000 and there is no way to make change. Want to buy a newspaper, a drink in the bar, or a t-shirt? Well you have a $1000 bill, those things are free. Want to buy a new suit or rent a hotel room downtown for one night. Make a wealth roll. If you roll good, its free. Roll bad and you just spent $1000. No sorry you can't get a new suit for less than that today.
I'd rather have more detail and actually track coins, items of value, etc. in a game where accumulating wealth is an object of play or I'd rather have less detail and totally hand wave wealth without the need to track levels.