Certainly, some aspects of the means that Edelgard uses are questionable. Even her Battle of Eagle and Lion interaction with Dimitri is harsh, if you ask me. It absolutely makes her ambition strong, but to someone who isn't there to see her develop, questionable. If they weren't, the decision to join her at the end of Chapter 11 would be too easy to make; as in, the Church gets your support if it were that easy.
That said, I would argue the actual villain is the Church, who you may replace at the end of the others, but still remains in power. This is something that Edelgard seeks to end. This seems clear to me because of a few reasons...or maybe more than a few:
1) Jeralt specifically (at least in the BE route, I haven't played the others...simply read about them) tells you that he doesn't trust Rhea, and he eventually flees in order to escape her influence. This is also something that Rhea hides from the others involved with the church, and Byleth. It's manipulative, and her goal to effectively coax you to continue her legacy. Make no mistake, Fodlan is literally led by a mix of Church and State, and Rhea wants it to remain that way, no matter who she has to crush or silence to make sure it happens. (In addition, despite her "motherly" demeanor toward you in the story, she uses Byleth as nothing more than a tool, if her reaction to the player siding with Edelgard is anything to go by. It is a facade only to be, potentially, altered to be more genuine later on if the player sides with the Church, which is what Rhea seeks: control over her "experiment")
1.5) Sure, the Dragons gave humanity their power and a gift so that they may exist in harmony. That does not, despite what some people may say, excuse the exploitation of the system and oppression it causes. The only reason I mention this is because I've seen some folks say, "How could you kill Rhea? She and the dragons provided so much for Humanity!" While this may be true, it doesn't mean that humans must take the oppression of those who bring them "peace and freedom" if it is no "peace and freedom" at all.
2) Rhea rules with an iron fist. She sends students of the Monastery to go out and crush those who might go against the church. This is also done in order to "send a message" to the students to never move against the church. It's basically fear mongering, meant to discourage those who may think differently from rising up and making change.
3) In the BE route, Edelgard (and Hubert) both have regrets about siding with Those who Slither in the Dark, but it is an alliance they needed to create in order to succeed. They operate as part of the system Edelgard seeks to destroy, but they cannot win a war with so many sides against them.
4) On top of that, Edelgard and Hubert start the war because, frankly, it's the only way to actually force change in Fodlan. Dimitri would not have started a war to change the status quo. Claude would not start a war to change the status quo. There is no way that Rhea would fold to a diplomatic discussion, as it is clear she favors her power and is not going to give it up so easily. The only way to actually begin to make change, to buck the reliance on Crests and the suffering it brings (especially to all of the students who suffer from it) (As a teacher myself, this is actually quite similar to how particular parts of the education system are structured, in that it isn't meant for students to make change, but rather, in some cases, learn and regurgitate information...which by all means keeps Rhea and the Church in power in the context of Three Houses. Again, Dimitri doesn't rise against that without the actions of Edelgard, for example.
5) It's clear throughout the story of the BE that Edelgard takes absolutely no joy in the war she started, as she not only says, "You didn't fight in vain!", in some fights against enemy soldiers during Part 2, but actively and vocally asks for her peers in war to live through to the other side so that they may enjoy the New Age of Fodlan together. Incidentally, she actually voices interest in not even ruling once the war is over. She doesn't even necessarily want to be a leader. In the BE route, it's not about the power. It's about change and justice.
6) While Edelgard does keep her actions a secret from you during the BE route as the Flame Emperor, she does indeed stand up to Thales and Kronya after they murder Jeralt. Whether that may be blamed on naivete of a young ruler-to-be for trusting these folks, who play tricks on her as well throughout the story or the fault of the system that failed her, and several other students, is up for debate. I've read that the information she claims to believe, such that Nemesis was falsely portrayed as evil, is misguided and was told to her by Those Who Slither, which I attribute to naivete, and confirmation bias on her part. That, I disagree with.
7) Another aspect I find people give flak to Edelgard for is the fact that she didn't try a diplomatic approach, but I don't see how that's at all feasible considering who we're talking about. Not only does she show her hand politically with what her intentions were, but if she suggests this idea to her professor, she risks getting talked out of it, or reported by those who may fear the idea. She can't go to Dimitri because she knows he despises her (for reasons he has been misled by, mind you), and therefore must oppose him. The Dimitri of the BE timeline effectively embraces sadness only for Dedue, but not much else. Yet, Edelgard still feels compassion for him, and through this compassion, ends his suffering by ending his life, as he has become blinded by revenge. Unfortunately, Dimitri could have gotten his revenge if he sided with Edelgard and took down Those who Slither, (though this is just like how Edelgard could have taken Dimitri's hand at the end of the BL route...though knowing her ambition, she would never be satisfied with the outcome Dimitri produced).
8) Not really a point in favor of anyone, but the outcome of the game is largely obviously determined by who the professor guides. Edelgard is a tragic story of unchecked ambition if Byleth doesn't side with her. This is basically similar to Daenerys Targaryen of GoT. She's absolutely fortified in her own resolve; but without guidance she can achieve little. As she has the most clear ambition of the three House Leaders, having the guidance of the professor allows her to achieve quite a bit, when combined.
Side note: I will say, I realize there's no "canon route". However, the way that Edelgard and the Black Eagles route are being pushed (one example: Edelgard evidently already has a Figma in development), it makes it seem that the developers see her path that way; or more directly "canon". I'd argue that her path being the distinctly different one, regardless of animated cutscene quality, suggests this as well. In addition to the fact that she is the only other bearer of the Fire Emblem, along with Byleth, it certainly seems as though this may be the "canon path". I can't objectively prove it, but those are my thoughts.