Requiring a "you" as a killable character in the game is not fundamental to RPGs. Am I misunderstanding your position? Because if not you're saying that Icewind Dale, the entire Wizardry series, Dungeon Master series, Wasteland series, and on and on and on are not RPGs.
Yes, it is fundamental and yes, you do exactly that in all the games you mention.
You even create your character yourself - nobody says you can only be one character.
And when "you" die, it's all over (well or you reload, but you know what I mean).
In BB, there isn't any "you" that could die to result in an end state, no "you" that is elevated above other characters in the game, no "you" that has any impact on what is happening on the battlefield beyond "player is playing the game".
You are not that recruit you just hired a second ago and who will most likely get killed horribly in the next mission. Those are just pawns.
Again, except that game mode where suddenly there IS a "you" whose death results in an end state, one that IS elevated above the pawns, one that HAS an impact on what is happening beyond "player is playing the game".
BB has a lot of RPG to it, same as other tactical games do. But it is not a pure RPG, it's a hybrid like so many others.