No doubt mouse is better, but it's by no means realistic. Nobody can move their head as fast as one can with a mouse. The controller implements inertia that adds some realism to our characters. That said, the controller requires something the mouse doesn't - not just fine motor skills but also fine timing skills. To move our head / gunsights with a controller, you have to push it in a certain direction for a specific amount of time and stop. A mouse just needs to be moved to a predefined location IRL to correspond to a point on the screen, which admittedly is more realistic to how moving our actual heads / hands work. Though after years with the controller, this timing becomes second nature.
It took me a long time to "git gud" with a controller, and even then there are limits. I definitely don't have the fine control aiming rails in FA-off using a controller that I would with a mouse, for example. I don't know if a HOTAS would be better or worse. Then again, I have no interest in flying a spaceship with a mouse, LOL. And as I previously mentioned, when playing PvP on console, everyone is working with the same physical limitations, so while it may be harder for me to snipe, it's also harder for someone else to snipe me. There's nothing quite as frustrating as being insta-sniped on PC because someone is using a gaming mouse with programmed curves and perhaps even cough, cough an aimbot, cough.
But I know where you're coming from, because I fought against console myself in the early days, using many of the same arguments you and others are making. The majority of my friends were on console, however, and PCs have their own negatives, so I made the switch and all these years later very much enjoy my overall gaming experience.
