Turns out if you have a button to do the same thing, once the user enters immersion the actual control becomes less important. Where alternate hardware is useful is for more analog controls that a joystick/mouse can't easily simulate.

Thumbsticks typically[^] have a button in the base, they're often used for this since one doesn't need to move off the stick to use it.

[^] Nintendo is a holdout here, though the WiiU apparently has the buttons.