I've never understood the hate for so-called "animation priority." It seems less like animation priority and more like common sense. Taking actions take time, whether swinging a sword, reloading a gun, or crouching. I just don't get it, how else would you expect these things to work?
I think it's sometimes the inability to get out of the animation that becomes the problem. The inability to interrupt yourself.
To me Animation Priority has become another way to do combat, and nothing else. It's not bad, it's just preference. It's totally reasonable to hate it. The most obvious examples, the Souls games, do it really well. Surprisingly enough, Dead Rising 1 & 2 also heavily rely on animation in combat.
In these sorts of games, a significant part of the strategy is to know how long an animation will take, and plan attacks accordingly. I love it :)