Kiran (Heroes)
Kiran is literally an isekai protagonist with zero personality and a barely-there presence in the story, with next to no customization to speak of. They're present as the stand-in for the player in this goofy crossover mobile game and that's about it.
Mark (The Blazing Blade)
Mark was created as an avatar for the player given that The Blazing Blade was written with series newcomers firmly in mind. That being said, their presence in the story is barely above Kiran's, their sole physical presence in the game is a map sprite with no definition, and their characterization is that they're a tactician that just happened to meet Lyn one day. You can give Mark a name, gender, and a birth month (or a blood type in the Japanese version), but that's about it. Their ending is, however, dependent on how skilled you are at the game.
Kris (New Mystery of the Emblem)
I actually don't know much about Kris since I never played New Mystery, other than the fact that they're the prototype for Robin and Corrin. I'm not sure that New Mystery needed an avatar unit inserted into it, but on the other hand, Shadow Dragon was bland and lacking in basically every improvement it desperately needed and that New Mystery got.
Corrin (Fates)
Corrin Discourse has been completely and utterly exhausted to the point that all that's left is an abandoned strip mine, and the less that this thread gets derailed by more Fates talk, the better. That being said, Corrin's default appearances stand out and the attempt at making an avatar the actual lead was an interesting idea even if it was complete sabotaged by the general quality of the writing. But Corrin is also one of the best and most unique FE characters in Smash, so they've got that going for them.
Robin (Awakening)
Robin exists in that weird space where they're just as customizable as Corrin and play a vital role in the story, but without actually being the lead. And this is despite the fact that the game's actual lead (Chrom) is comparatively dull. Robin is an interesting character, but like Mark, is a tactician of inexplicable talent despite being found in the middle of a field with amnesia. Robin is entertaining and easily the best of any of the previously stated characters, but there are elements that just feel too convenient (and also, there's time travel involved that gets convoluted if you think about it too much).
So why is Byleth better than any of these characters? For me, it comes down to the full combination of their presentation, personality, history, and interaction. And yes, I realize that Byleth is a mostly silent protagonist cut from cloth similar to that of Persona and other JRPG characters. You can't customize them beyond name and birth date, they don't have voiced dialogue outside of battle or increasing skills through tutoring, and why in the fuck would the church name a mercenary barely over two decades old an academy professor?
But it really becomes clear why things are the way that they are the more you learn about Byleth. Because Byleth basically, would not be alive if it weren't for actions Rhea had taken in transferring Sothis's Crest stone from the heart of their mother to their own heart. They were a still born baby, and even after their revival don't have a heartbeat or a capability for strong emotion. Byleth is a broken person caught between Rhea's desire to see Sothis and Jeralt's unknowing fear of what Rhea had done, not realizing that Byleth would otherwise be dead. So they end up getting raised by Jeralt as a mercenary. An effective one with a reputation and appropriate nickname to go along with it.
Byleth is just such a strange, tragic character because of who they are. They aren't the heir to some peculiar invisible kingdom or the alternate timeline version of an ancient Fell Dragon's vessel that's actually with the good guys. Byleth is a vessel for the progenitor god, sure, but that status comes with a lot of personal costs to them in addition to the benefits. Robin can kill their alternate timeline self no problem and come back from it with no issue, and Corrin is too perfect. Even after coming into their full power, Byleth is a weird doll-person whose choices always result in tragedy because there is no timeline in which they can save everyone (even if you try to game the system and recruit as many students as you can). The continent would be absolutely fucked without Byleth, but in no case do their decisions result in a magical cure-all.