Anyways I don’t mean to invalidate your comment on wanting customization I completely get it, but just wanted to share my thoughts on why they likely haven’t been doing it lately.
No worries; everyone doesn't need to have the same opinions. Anyway, I don't mean to be pedantic, but I did say old
er, not old; as in, Awakening and Fates are older games than Engage and Three Houses.
When it comes to the games that are older than Awakening and Fates, I have only played Fire Emblem 7/Blazing Sword all the way through. I actually like the player avatar in that game maybe the most, as far as characterization goes; I felt it was fairly easy to insert myself into the role of silent tactician, and I felt connected to the other characters in the story without having to be forced into the role of chosen one. The only thing that I was sad about was that I couldn't participate in combat as a unit. So when Awakening came out and let me do just that, I was ecstatic.
I agree that the characterization of the avatar in Awakening and Fates is quite weak (I actually rather strongly dislike how 'Corrin' is written in Fates, in particular). The appeal of the customizable avatar in those games is that, for me, I like to make OCs and those games allowed me to make OCs that could actually participate in combat as playable units. Yes, you can say that these characters are Robin and Corrin and not whoever it is that I was making, but I could mostly ignore the main story and focus on my own head canon for these characters. Starting with Three Houses, this option was taken away, and thus I lost interest in the series moving forward; the appeal was gone. I could no longer be either a self-insert (like in Blazing Sword) or make my own OCs (like in Awakening and Fates).
Personally, my ideal situation would be to not even have customization tied in with the avatar at all, but rather end up something like Final Fantasy Tactics, with the ability to create generic units. That way they can still characterize their own characters the way they want to, and I can still make my own OCs as part of the army without also having to have my characters shoehorned into the role of chosen one, or otherwise characterized in an unsatisfying way.