Let us be clear on one point - the Federation ows the cardassians ABSOLUTELY NOTHING!
More than one time in the past, the Federation tried to build a peaceful relation to the cardasian union - and each time, the cardassians met these attempts with scorn and aggression.
And now, after the latest (and gravest) cardassian aggresion against the Fedetation is over, the cardassians expect the Federation to fight wars for their sake? The cardassians think they have THE RIGHT TO ASK THIS OF THE FEDERATION?

The Cardassians probably ask or expect NOTHING from the Federation. If I were to hazard a guess, most Cardassians are more likely to expect the Federation to do exactly what you're suggesting. Apart from a possible minority that might believe that Federation really sticks to it self-proclaimed ideals, it's more likely that most Cardassians are used to thinking about the Federation as another enemy empire bent on expansion, as hostile to Cardassia as the Klingons or Romulans, only more hypocritical about its motives and methods. An opinion which the Federation would confirm by doing what you suggest.
It's the Federation itself that should ask and expect itself to behave differently, if all those proclamations about Federation ideals and morals have any basis in reality, and unless Federation and Starfleet authorities aren't just nothing by big hypocrites.
About the Federation upholding its ideals - the DS9 scenarists (and, to a lesser extent, the TNG/etc ones) were inspired enough to NOT make the trekverse a morally perfect universe.
That is, sometimes, the choice is the lesser evil between two evils.
An example - the Federation allying itself with the klingons, despite the imperialistic ways of these klingons - a continuing federation/klingon war would have caused much more death and suffering than this alliance allowed; indeed, there are signs that, recently, the klingon empire started to adopt more humanitarian values, or, if you prefer, that 'honor' started to become more than just a convenient excuse for anything.
Other examples - The Federation didn't attack all powers who acted contrary to its ideals, in order to stop their immoral ways. You see, that would change absolutely nothing, besides creating more death and suffering and leading to the fall of the Federation due to numerous wars.
At present:
"The Klingons and the romulans will definitely want their share of cardassian spoils of war. And if the Federation refuses, it could lead to a new war - at the very least, a new cold war - between klingons, romulans and the Federation."
Morally, a war - or cold war - between the Federation and klingons/romulans would cause much more death and suffering than giving the klingons and romulans the gains for which their soldiers died (I guarantee klingon/romulan soldiers didn't die in order to uphold moral ideals).
As for the rest - you say "The Cardassians probably ask or expect NOTHING from the Federation."
Good.
This means the cardassians don't expect the Federation to fight a long, bloody war for them, federation citizens to die just so that cardasssian teritory doesn't go to klingons or romulans.
It also means that when klingons and romulans occupy their share of cardassian real-estate, cardassians won't go on an egocentric, arrogant tirade of "~Why doesn't the Federation fight them for us! The Federation has the obligation to fight our wars for us - because we're cardassians!
If the cardassians think "about the Federation as another enemy empire bent on expansion, as hostile to Cardassia as the Klingons or Romulans, only more hypocritical about its motives and methods" because the Federation doesn't send its citizens to death, doesn't provoke the maximum possible amount of death and suffering for the sake of cardassians who just tried to DESTROY THE FEDERATION, let them think so. Contrary to what you think, it doesn't make the cardassians right - NOT EVEN CLOSE.