A more likely reason would be Orion/Ferengi economic interests in destroying the Federation; they are capitalist in nature and the UFP is -- at best -- socialist. There's an inherent conflict of interests. The Ferengi, driven by profit, probably put out a sizeable amount of entertainment; in a century where work is passe and everyone is cared for, entertainment is going to be job 1. They could use this control on media to slowly undermine the confidence in the UFP, by hammering home to the planets that were abandoned/invaded during the war how little the Fed did for them. The UFP would be on a massive rebuilding process after the war; the amount of resources that would have to flow to the center -- by the very nature of the centralized, non-monetary economy -- would be a drain on a lot of the newer or fringe worlds
Yeah, yeah...the economy of the Fed is based on the replicator, which gives unlimited production capacity. Bull. It still requires energy. Energy still requires you to burn something, ultimately -- you might get away with the solar-powered utopia, but it's unlikely that you could put enough solar collectors to power the computer-intensive, transporter/replicator intensive Fed society. Matter/antimatter is fine...but you still have to collect hydrogen, use energy to make antimatter... Ultimately, there's a cost/benefit point where just replicating certain stuff isn't cost effective. The point being: the member worlds are going to have a higher drain on materials and 'monetary' resources; this has a tendency to tick off people who aren't seeing immediate benefits of such spending.
STVI gave a good impression of how some other alien cultures might view the Fed: as a 'humans only club'. People stuck in dead-end jobs because Vulcans live so long they can hold high offie forever might view the Vulcans the same way. Most of Federation law seems to be a mish-mash of socialist humanism and Vulcan asceticism and non-intervention. Not always an attractive thing, if your from some lowly third tier world, looking to exert a little influence int he Fed Council. (If you're not from France or Germanhy in the EU, you'll get my point...)
There's all sorts of ways the enemies could exploit inherent weaknesses in the Fed. Diversity is a sign of strength to a point; then division creates lack of cohesion. The Fenergi & Orions are also the kind of 'secondary threat' that every one pooh-poohs...'til it bites 'em. The Romulans would be particularly good at exploiting this sort of thing, I think. It would allow you to keep the Federation as a gleaming example, being attacked from within, but due to external forces.
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill