I'm not saying the Ascians aren't antagonists, but their reasons for doing what they do haven't been explored yet beyond "Hydaelyn is bad and we need to resurrect Zodiark to off her." While what they do is very detrimental to us personally, on many levels, we still know very little about the big picture of what's going on with Hydaelyn (the Goddess) and Zodiark. Thus while their goal does seem to be genocide of all the mortal races on Hydaelyn (eventually)... the why is the big question.
Good villains aren't the kind who sit around thinking of ways to be evil. They're normal people forced into it, be it by their own personality or the situation they're in. Granted the Ascians are nigh-immortal sorcerers who command magicks far beyond mortals, and all of them (save perhaps Elidibus) fail to have any sort of sympathetic personality), but that still leaves their situation ambiguous. Why they believe Hydaelyn is a parasite that has to be burned out or the physical and aetheric planes will get messed up, why they need Zodiark back, what resurrecting Zodiark will do to Eorzea, what happened to Zodiark in the first place... etc etc. There's too many unanswered questions to just label them "generic evil overlord(s)." That's taking the easy way out.
As for Hydaelyn, the road to Hell is paved with good intentions - just because you mean well doesn't mean you do well, and what Hydaelyn's been doing doesn't sit well with the Ascians. Why?