You do know that first-person shooters, even very fast-paced ones where you run around at completely superhuman speeds, have existed for VR for many, meany years now?
Yes... and many of them are vomit-inducing nightmares for a large proportion of the population.
It's a solved problem. Where are you getting this idea that you have to run in real life in order to run in-game? You don't have to do that in non-VR games. Why would VR games be any different?
It's hardly a "solved" problem. Most games still use teleportation to move you around the field for a reason. When there's enough desync between what the inner ear is experiencing, and what the eyes are seeing, the brain thinks it's been poisoned, and tells the stomach to vomit. For most players, having a cockpit around them is enough to prevent that desync, but for many players the SRV still induces nausea.
Roomscale VR (which has its own set of problems, though those are actually solved, just require a great deal of work to implement) remains the best way to prevent nausea for the largest group of players.
The ONLY difference between non-VR and VR FPS games is that, usually, the camera is rotated in steps rather than contiguously, in order to avoid nausea (although most games will give you the option to turn contiguous rotation on if you so desire.)
Stepped turning...

Why are many people here talking as if first-person shooters, including those where you run around large distances very fast, do not exist on VR?
Because there's a huge difference between good implentations of such gameplay that works for a huge group of players, and ones that work for a small subsection of the population that isn't sensitive to forced rotations.
edit: just noticed the date of the opening post. Is this a Zomba thread ???