Well, one thing the Federation can't do (at least any more) in that scenario is whistle up your "friendly neighborhood Klingon task force" for backup if things get hairy (as Picard did on occasion and Sisko did fairly often). I think that it is this lack that would have the biggest impact on the Federation, as it takes one more tool out of their crisis-management kit.
The other big hit would be that Starfleet would have do divert resources to once again patrolling the Klingon Neutral Zone. At that moment, the Klingons wouldn't have the strength to invade (they took crippling losses too, as DS9 showed), but you couldn't count on any passing Klingon battle cruiser to be non-hostile any longer. I would see the "new" Fed/Klingon relationship as being basically the same or a little more strained as it was in the late 23rd century before the First Khitomer Accords.
The Cardassians are a different kettle of fish juice. The Allied Powers are keeping the Cardassian Union well under their thumbs, similar to the way we did to Germany and Japan after WW II. The Federation is going one step further and trying to actively retrofit and rebuild Cardassian culture along more socially acceptable lines. The Cardassian ensign I mentioned doing RIP would be emblematic of this. That would be a source of contention both within the Federation (some would prefer a harsher tone be taken), and within Cardassian society as well.
I could see the Romulans in part taking on the role you are suggesting for the Cardassians (as they do in the novels), making the new Alliance/whatever more of a client state or cutout/stalking horse, a la North Korea and China.
The other big hit would be that Starfleet would have do divert resources to once again patrolling the Klingon Neutral Zone. At that moment, the Klingons wouldn't have the strength to invade (they took crippling losses too, as DS9 showed), but you couldn't count on any passing Klingon battle cruiser to be non-hostile any longer. I would see the "new" Fed/Klingon relationship as being basically the same or a little more strained as it was in the late 23rd century before the First Khitomer Accords.
The Cardassians are a different kettle of fish juice. The Allied Powers are keeping the Cardassian Union well under their thumbs, similar to the way we did to Germany and Japan after WW II. The Federation is going one step further and trying to actively retrofit and rebuild Cardassian culture along more socially acceptable lines. The Cardassian ensign I mentioned doing RIP would be emblematic of this. That would be a source of contention both within the Federation (some would prefer a harsher tone be taken), and within Cardassian society as well.
I could see the Romulans in part taking on the role you are suggesting for the Cardassians (as they do in the novels), making the new Alliance/whatever more of a client state or cutout/stalking horse, a la North Korea and China.