Keyboard and mouse players should not have such an advantage with sensitivity over game pad players. Also its not realistic for the avatar to turn a complete 180 in a nano second, its not realistic and is an unfair advantage, If realistic is what your going for every player should not be able to rotate so fast or atleast with limits that is more realistic or damn just fair.
Mouse and keyboard are just better for FPS and will always be. You can always up your control sensitivity to the wazoo to get faster response from the pad but it comes with other tradeoffs.
Now, doing something "realistic" with the character rotation or aim movement rates is rather more complicated than just limiting it.
And doing full 180 degree turn is actually quite quick for a human to do as long as they're not having the gun up in the "on target, ready to fire" -position (vs the various "ready" positions as referred to in most forms of firearms training) where the extra mass far away from the rotational axis will add a fair bit of moment of inertia (also it's super bad form to barrel sweep like that if we're talking about real weapons)
To be fair I've seen some pretty crazy stuff done with a gamepad, but those people are all the way right on the skill bell curve.
Playing FPS on a gamepad is just a very bad idea unless you happen to have sensitivity and coordination of this guy (and crazy quality pad that can actually accurately and repeatably measure tiny movements)
Modern quadcopters with their MCU assisted control (at the very least, can't control one without) and very fancy computer control in case of DJIs for example give people completely wrong idea of how easy it's to fly a traditional configuration of RC heli, it's super hard, and keeping one hovering stable so close to the ground (in the "ground effect") takes a metric ton of skill (my olskool heli is basically permantently "under repair", the Mavic on the other hand is trivially easy to fly and even if I sometimes break props they're cheap [even the DJI originals] compared to size 500 heli main prop blades).
edit: the RC controller is basically a fancy gamepad, two sticks and a bunch of switches.