If you're a main FE character, and especially one that has your mug prominently featured on the front cover of your game, you're overwhelmingly popular by default. That's indisputable.
Now I can't speak to Edelgard's characterization in Three Houses since I haven't played the game and don't plan to anytime soon, but she could literally have the personality of a cardboard toilet paper tube and she'd still be popular.
As another example, just look at all the samey and derivative royalty in the series that folks go crazy over, not to mention characters that have little depth to them beyond a defining quirk. And I mean no offense to anyone by saying that, coming from a guy who considers Est as one of his favorites despite a personality that's summed up as "I'm the youngest Whitewing and I like to make stew!"
