Here's the `invert mouse` setting from Quake2[1], though, I know for certain that Duke3D and Doom had the same option. I feel like every FPS I've ever played has had it as an option.

Now, to be judgemental, anyone who enables the invert option is an obvious psychopath. Although, to be fair, everyone thinks I'm a psychopath for using Mouse2 for Forward.

[1] http://www.quake2.com/kko/menu/options.jpg

Doom didn't, since it didn't support looking up and down.

"Shearing" was added for up-down look in Heretic, for the non-Doom engine descendants Duke Nukem 3D and Rise of The Triad supported it as well. I don't remember if it could be bound to mouse movement in any of these games.

They were bound to keys for the DOS versions from memory. Forget when the mouse look was supported but the view was highly distorted so mostly useless until later ports enabled proper 3d rendering.

Oh come on. I’m a pilot, or at least I spent a good deal of time in flight training when I was younger. I’d rather not mix systems, that’s all.

Yeah screwing with your muscle memory is a really bad thing to do for pilots because that will be there for you when you need it the most.