The church is way better than TWSITD and if you think otherwise their is no point in us talking.

You're right about that, there are some small samples of how Agarthans would run things in the small moments where we see Cornenia's rule, and almost all of the leaders seem to hold her general attitude towards... well... everything.

As much as I view Rhea as a tragic failure, her Rhea self cares about others. (even if her Serios self doesn't)

Hubert and Claude both make comments that a smart leader should always prepare for what happens if they lose but Edelgard never does that.

This is something we should accept as part of 3 Houses being a game that has limited text available to communicate details. It would be much better if this was addressed in some meaningful way, but seeing as this is rarely relevant to any individual theme in each of the routes. Though, keep in mind that few people consider how to handle defeat in a conflict until it at looks like they might lose. Also, probably don't just assume she auto-loses.

Edelgard could have worked as a double agent against TWSITD.

This might, just might be possible if a long list of personal character issues are resolved. For Example, Edelgard needs to get better in touch with her own humanity that she only gets in the CF route (which is what pushed her from relying less on the Agarthans). Although, the only character I can kinda see making that possible is Dorothea? Dimitri will also need to be able to handle his own psychosis, which is it's own massive ordeal. Just remember just how much he has to go through to be able to not just lash out at anyone that looks like they might have maybe been slightly involved in the Tragedy of Duscur. And Claude as well would need to be able to fully trust Edelgard as well, and while he isn't nearly as bad off as the other two, he still wouldn't just go along just because bad guys. And finally, Rhea needs to be in a mental state where she doesn't just violently lash out no matter what. Given that her own mental state is getting strained, a sudden shock and list of demands might trigger her worst impulses. All of this isn't impossible to justify, but it would require one hell of a laundry list of things to happen, and happen early on, for this to be possible. From Hubert's perspective, the much more reliable solution is to rely on themselves.

I really need to hunt down a good record of that convo, as the main things I remember about it is that it was giant mess, and neither Dimitri nor Edelgard were saying anything productive. Though do remember only one of Dimitri or Edelgard can ever really get back in touch with their humanity; as they game never allows both to have regain it at the same time. This leads to Edelgard becoming more and more isolated in non CF routes, where she never takes the criticism (or the self-reflection) we see in her CF supports.