My take? Alear is not an Avatar. They are a player character, but not an Avatar. Alear has a fully defined character and a minor arc as well. I could say the same thing for Shez. Byleth is... a different issue. Byleth is a character, but the game very much refuses to acknowledge that, both because they barely speak or emote, and even the captions call Byleth "Professor" or some other title. Like... at least Engage had the dignity to name Alear in subtitles sometimes. As such, despite being in the same mold as the above two, I don't connect with Byleth as much.
Customization is what makes an "avatar" for me. Can you really say Byleth is you? Can you say Alear is you? By comparison, you can alter the appearances, stats, and (in the 3ds games at least) even voice of Kris (again, voice doesn't apply here), Robin and Corrin, so they feel like your character. And in Robin's case, despite having a defined character, doesn't have a character that is overly pandered to as the "real hero" like Kris until the end, nor do you feel insulted by their character because the writers played it too safe like with Corrin.
But you don't need customization to slot into a Fire Emblem character. You can do that through a player character that isn't an avatar. Case in point? When I played the first act of Shadows of Valentia, I felt like I was Alm. I've said this in the past, but in Alm's side of SoV you really don't feel like you're controlling Alm. Maybe I'm just a sucker for the awkward everyman. It felt a lot better than when Celica was in command.
At their core, Fire Emblem games are strategy RPGs, and roleplaying involves feeling like you are that character. It's much easier to feel like I am Robin, or Alm, or Alear, and I actively feel like I do them. When I'm controlling Corrin, Celica or Byleth, I don't think, "hey, that's me," I think "hey, that's my lord" and I start to treat them differently.
âĶI might be far off topic. My take is, I really don't care whether avatars are customizable. It'd be nice, but not necessary - Alm proves that by not being customizable at all (granted, he's the main lord of a remake, so that was never going to be an option). Just make them a character I can get in the mind of... one I can truly *feel* like.