FE3H is literally a game about contrasting values and leadership types, explored dually with the structure of an ancient and deeply organised institution. The parallels are undeniable. However, I would point out that the game is limited by the blinkers of its authors (horseshoe theory), and thus Edelgard's dual appeal towards the utter dregs of humanity and politically-inclined sapphic girls has nothing to do with her coded energies or intense fixation with Byleth, but instead her radicalism in a time of polarity and conflict. However, in times of polarity and conflict, such institutions often uplift themselves and hijack the energies of the youth via stealing the signifiers of their opposition, muddying the water, diluting the meaning of anything 'radical', and rendering the debate as one about aesthetics rather than meaning.
While it's true that Edelgard ultimately upholds the paradigm of the establishment she seeks to overcome, and the Black Eagles route fittingly ends with some ambiguity as to how successfully she will navigate the tension between power and emancipation, I would instead suggest that Hillary Clinton is better represented by the character of Rhea.