To me, there’s a difference between “twitchy” – your typical MP shooter these days – and “fast”. I consider “fast” in things like Painkiller and Quake et.al. where you’re just barreling along, mowing fools down, switching weapons, and getting into a good rhythm. My reflexes may not be at their UT’99 peak but I still enjoy speeding around a level constantly blasting idiots, broken by the occasional respite. The shooters that get that “fast/slow” pattern are the best for pure shooters.
(That balance is tricky; PK got it right IMO but not Serious Sam, which kept its fighting periods up so long they were tedious).
Doom 2016 curb-stomps D3 in every single respect. I played through D3 some years ago more because it was the most technically advanced shooter out there, rather than actually liking it.