I guess my generation likes teams more than individual players. When a player from my team leaves, for example Betts, I couldn't care less about him. I personally would never 'like' a player on the Yankems, but, at the same time, I can respect that player, for example, Jeter.
Btw, my favorite player on the planet right now is Devers, but what the hell, I'm a SOX fan.