gnatSome of the lack of variety in movement-shooters is also probably due to how consoles rule the video game market and the need to make games that work with their input methods (controllers). Things like air strafing and rocket jumping don't really work when using a controller.
This leads to less skill-expressive movements like "press x to rocket jump", slides and wall-strafes that have less depth than games designed primarily for mouse and keyboard.
I think new input methods may well lead to more creative and higher skill ceiling FPS movement design.
the fucked up thing is modern controllers are fully capable of competently playing fps games with gyro input but controller players are whiny little babies who refuse to have the game not aim for them to compensate for their ridiculous fake controls, and devs are too cowardly to force them to actually play the game themselves
still, even pc-exclusive "movement shooters" are largely really bad due to the lack of camera movement based techniques other people already mentioned. without involving the mouse, the only thing a keyboard and mouse input based game can ever test the player on is timing of inputs, as soon as you involve the mouse everything becomes so much more granular and engaging