I can buy that they'd want to fight back against the empire individually. I can't buy that they'd cooperate with each other as a party, much less all be onboard with what they decide to do.

They just don't feel like human beings. For instance, I'd imagine Edgar to be much more concerned over how matters affect Figaro and South Figaro even beyond what happens with the empire, Strago to be much more concerned with not putting Relm near any mortal danger, while I'd imagine Cyan to be much more concerned with inflicting as much damage to the empire as possible no matter what. There's not much of a common goal there and it'd almost certainly lead to strife and disagreements, especially in the absence of a leader they both trust, which FFVI's party lacks. Fortunately they all just go along with whatever the group decides to do, and I'm not sure these three ever exchange any more than five lines of dialogue beyond maybe pleasantries/introductions. I'm not even sure if the others know Edgar is a king, come to think of it. And even when the empire stops being a threat, it's not like, say, Cyan's arc involves him learning from someone else in the party, or someone else in the party learning from him, or talking with him, or acknowledging and caring about anything he's going through. It's in total isolation from the rest of the group. He, as a character, in general, exists in almost total isolation from the rest of the group. And the same can be said for most others.

The scene I always think about at times like these is when in FFX Yuna considers actually ending her pilgrimage, and her and Tidus together actually go through how every member of the party would react and feel about this decision each for their own reasons.

I agree it's a limitation of the times, maybe it was even a necessary step in evolving, and sure enough, the series got so much better about this in the PSX era, especially by FF IX. Which is why I tend to prefer those games' casts as well as other SNES games like FFV and Chrono Trigger that at least played more to the strengths of that era rather than playing hard into its weaknesses.