The thing is she could have accomplished almost all her aims without the continental wide war.
-Prosecute anyone involved with the crest experiments performed on her and her family.
-Ally with the Church and other nations to get rid of TWSITD.
-Implement laws banning discrimination based on crests.
-Employ Hanneman and like minded individuals to create weapons comparable to crest weapons for the crestless.
-Discuss with Dimitri/Claude how the crest system is ruining their societies and how measures need to be taken to fix this issue. Claude is basically already seeing this. Dimitri may need more coaxing, but seeing how in Azure Gleam he employs Miklan to prove that people without Crests could be just as capable as people with them, he is also of the same mind.
That just leaves the Church around, but most of the problems it generates disappear if people quit worrying about crests. Edelgard also could decide to ignore the Church's rulings that keep technology stagnant and allow society to progress. Rhea may be mad, but she isn't going to declare a war over it.
Of course, we don't get Three Houses if El doesn't choose violence...so she is a tragic antagonist to give us one of the best Fire Emblem's to date. Oddly enough, in Crimson Flower the world ends up better than it was before post-TWSITD being defeated, but yeah, it took a war and a lot of deaths to do it.
I'm...the...master...of...ellipses...