I've always had a bit of a problem with the single civilization powers like the Klingons, Romulans or the Cardassians seriously challenging the Federation which consists of more then 200 civilizations. But that's really an argument for another time. Clearly the Cardassians were dangerous but not overwhelming power politically or militarily. After all the Klingons did completely overwhelm their defenses fairly quickly. There is also the Cardassian war, first mentioned in TNG in "The Wounded." Interestingly though out of all the regulars on TNG, DS9 or Voyager, only Picard and O'brien seemed to have any direct experience in that war, which makes you wonder how widespread that war actually was.
There are hints at some sort of economic/ecological disaster that happened on Cardassia in the last several hundred years. Picard mentions in "Chain of Command" that Cardassia was once a prosperous civilization known for it's art and architecture before having some sort of catastrophe that allowed the military to form a dictatorship. I'm curious at why Cardassia would continue to struggle even into the late 24th century before the Cardassian war since it seems that the main resource in the 24th century is Energy. After all if you can transform silicon into gold or anything else you might need, the question of resources becomes very broad. And yet it seems clear that the Cardassian motivation for invading Bajor was economic. After all, Empok Nor/DS9 was designed primarily it seems to be a massive ore processing plant, but unfortunately it's never clear what ore (perhaps dilitium?) they were extracting. So I guess we have to take on screen evidence to mean that the Cardassians were lacking something. It also could come down to centuries of mismanagement by the Cardassian military dictatorship, even an enforced mismanagement to justify their continued control. After all if Cardassia is prosperous and the people have more economic freedom, they might start wanting other freedom as well.
Which leads me to think that Cardassia would probably still have the same struggles it did before, the pressures that led it to anex neighbors and strip mine them. Which means they will have to have some pretty dramatic changes to prosper. Japan after World War 2 might be a good model here. Japan is comparatively resource poor with a highly skilled population, which led it to start invading its neighbors during the 1930s for more resources and putting into a crash course with the U.S. After World War 2 Japan recovered at least in part by using its highly skilled population to manufacture while relying on other countries for raw materials. That kind of system demands the easy flow of resources back and forth between countries. That could easily come if Cardassia opened its borders (which previous to the Dominion War were highly armed and impermeable) and allowed free trade back and forth between them and the Federation.
As far as Elim Garak, I never pictured him as much of a leader. However I can imagine him as some sort of power broker working behind the scenes, kind of like a Shadow Shogun.
And while the Romulans and Klingons may be tempted to divide up Cardassia after the war, it seems like it would be a pretty difficult prospect considering the distance between those powers. While there are no official maps in Star Trek (beyond the vague ones that appear on various displays), most that I've seen including Star Trek Star Charts published by Geoffrey Mandel who worked on Enterprise and are probably the most comprehensive we have place Romulans and Klingons pretty firmly in the Beta quadrant separated from Cardassia and Bajor by a pretty big expanse of the Federation. Even if they wanted to, I doubt they would have the resources and will to maintain territory that far from their home space, especially if the only practical way through would be through Federation Space.
I would like to see where the Cardassians go. When they were first introduced they were one of my least favorite alien races on Star Trek, but over their time on DS9 I grew to really appreciate and love them. Some of my favorite secondary characters in Star Trek are among them like Garak, Dukat and Damar. I think they are among the most tragic civilizations that have been in Star Trek, ironically fighting for that spot with the civilization they ended up terrorizing, the Bajorans. But at least Bajor had something of a happy ending; Cardassia had centuries of poverty, war and sadness ending in the almost total destruction of their homeworld and the loss of over a trillion people.