Monetary wealth and the general economics of capitalism in the UFP is a weird concept and anathema to its general philosophy of personal growth. As I posted earlier, the UFP is a post-scarcity society where all the necessities and other "luxury" items are readily available and thus without much monetary value (how much do you think a TV would cost if all you needed to do was replicate one?). Things don't have any monetary value because they are so easy to obtain, and thus their value as symbols of wealth, influence, and status is practically nil. Instead, things have personal value that can't really transfer. And in a post-scarcity society, money has no value because the things you would potentially spend that money on has no value. This is especially true when you factor automation into the general resource economy. Therefore, it doesn't make much sense to have wealth as a measure in the game for the UFP. There may be something to it as a matter of resource scarcity on some frontier worlds, or independent colonies outside the UFP. The Orion Syndicate would probably use economics and wealth as a form of control, while the Cardassian use might take the form of social control and structure, as well as for raw political power. But such things I'd imagine are aspects of one's cultural values (i.e. the Ferengi).
That said, it would have to be replaced with something else that would effect the UFP. Happiness, perhaps, although that seems pretty close to unity. But if one's culture has low happiness, their unity would suffer as a result. Wealth could be useful for the Cardassians (their society is pretty stratified between haves and have-nots), the Ferengi (those capitalist rascals!), and perhaps the Romulans. It strikes me that Klingons might be in the same boat as the Federation, but just because they are all about glory and honor (there is no honor in accounting, after all). Wealth could be replaced with glory and/or honor, which comes through conquest of one's foes (or the hunting of targ and saber bear). Insufficient glory and honor, and you have insufficient unity, which leads to a civil war between the great houses.
That said, it would have to be replaced with something else that would effect the UFP. Happiness, perhaps, although that seems pretty close to unity. But if one's culture has low happiness, their unity would suffer as a result. Wealth could be useful for the Cardassians (their society is pretty stratified between haves and have-nots), the Ferengi (those capitalist rascals!), and perhaps the Romulans. It strikes me that Klingons might be in the same boat as the Federation, but just because they are all about glory and honor (there is no honor in accounting, after all). Wealth could be replaced with glory and/or honor, which comes through conquest of one's foes (or the hunting of targ and saber bear). Insufficient glory and honor, and you have insufficient unity, which leads to a civil war between the great houses.