Three Houses' conflict is an intentionally twisted and bloody Gordion Knot for which there is no allowed sword (read: golden route), which is part of what makes it so interesting and hotly debated (even if most of the debate is between stans eager to purport a "winner/best" rather than examine the conflict without the illusion that anyone was that). The developers clearly don't intend any route to be "correct."
Edelgard
and Rhea
both are simultaneously right and wrong, simultaneously responsible for good and bad, each with understandable motivations that tragically wouldn't have been mutually exclusive if they had simply laid everything out on the table with the goal of understanding and cooperation. In this, they are both at fault. (Claude and Dimitri are borderline irrelevant in the grand scheme of things by comparison -- neither would have opposed a more bloodless revolution of Fodlan's system.)
Much of Edelgard's understanding of history, and consequently her hatred of Rhea, is either flat-out incorrect at best, or TWSITD propaganda at worst, which she's at her most foolish in believing. Rhea is, of course, half responsible for this, because she and the Church are the ones who've falsified history (albeit in a bid of pragmatic selflessness). Already, that alone is a situation that's difficult to solve.
Edelgard, too, is the
only person in a position to enact social revolution in the way that she does. She is the only person intimately familiar with TWSITD's existence and abilities, and she is the heir to the largest country and military on the continent. People rightly praise her social ideals here, but unfortunately, as people praise Edelgard in one hand, they must malign Rhea with the other, when the reality is much more complicated.
Rhea and the Church are not responsible for the status quo of Fodlan's nobility, because they had no hard power to effect change like Edelgard did, and had to be hyper-vigilant against the threat of TWSITD. The crest-bearing nobility of Fodlan is literally condemned in the very bible of the Church of Seiros as the reason the Goddess disappeared:
The Book of Seiros said:
The descendants of the Heroes sought their ancestor's power, and thusly
their blood. In time, they amassed Crests, Relics, land, and wealth,
using all to set the land aflame with war. The goddess's power, intended
to stem the flow of evil, became a tool of destruction, all because of the
greed of humanity. The goddess grieved and, heartbroken, hid herself
in the heavens from whence she came…
Let's take a moment to allow that fact to sink in.
Now let's take a moment to remember two other facts: (1) The Knights of Seiros are a tiny elite force, incomparable to any of the three nations' militaries (see: the fact that they quake when the Empire's forces mobilize; the fact that they're so sparse they have to utilize military academy students to guard the grounds). (2) Dimitri's father, King Lambert, was assassinated by the nobility (abetted by TWSITD), establishing that the nobility will eliminate even the highest powers that seek to undermine them.
Edelgard was the key to the solution in all routes, but the tragedy is that her personal tribulations closed her off to anyone and hardened her against any questioning, which leads to her downfall in any route that isn't hers (because she didn't have Byleth). Instead, she sets up an elaborate and risky Xanatos Gambit whereby the country's sociopolitical state is improved at great cost regardless of if she wins or loses (hence why she throws the dagger at Dimitri in AM -- she knows she isn't long for the world in any case due to the experimentation, and thus forces Dimitri to solidify himself as a Hero-King by vanquishing the Emperor, rather than undermining his rule before it ever began by allowing such a controversial figure to survive).