This is a good example of having sound logic but not understanding the actual use case. It's simply a way to add functionality in a way to attempt to mimic what humans are capable of in a game. Not everyone wants to or is capable of using VR for various reasons. This allows you to use a slight physical movement of your head to replace using a mouse to move the camera, primarily in flight and racing simulators. That means you don't have to take your hand off of the racing wheel to move a mouse around, or even need to have a mouse available to you.

Is there a reason eye tracking can't work or doesn't work?

If you use eye tracking to control head movement then the head will move past where the eyes were looking.

People playing simulators such as DCS are used to have head tracking with OpenTrack. It's very helpful

Have you tried it or is that your theory?

Don't all headtrackers work like this? Also the infrared ones.

When I used a head tracker (homemade infrared one), I just got used to shifting my head but keeping my eyes on the screen. Having a wider screen helps.

I learned how to shift my head only a little bit to move the FOV a lot when using one of those infrared trackers. Still kinda hurt my neck.

Tons of people use head tracking like this via TrackIR and similar setups, it's quite common for space or air sim games.

And even with milsim FPS, as those blog posts from more than 10 years ago shows: https://dslyecxi.com/category/trackir/