Ah, yeah. Unfortunately I doubt it would be any better than a regular flat panel for simulation sickness in FPSes. (I very rarely play FPSes these days for the same reason.)
Unfortunately in first person games on flat panels, I know of 2 causes of simulation sickness: Unrealistic projection of the virtual world into your eyes, and, more significantly, the fact that the virtual camera moves when your head does not.
“Perfect” non-light-field VR eliminates the first problem in one way (X-Y) but significantly exacerbates it in Z (it still has no accommodation, causing the vergence–accommodation conflict) in a way that can only be solved with much better light field displays that we have today. It also eliminates the second, but only for games which do not have movement controls that apply extra acceleration to the virtual camera. (Steam VR Home, for example, never slides the camera - it only allows teleportation, significantly reducing simulation sickness.)
The Looking Glass slightly alleviates the first problem (only in X, not Y or Z/accommodation), but it can do nothing about the second problem because the screen itself doesn’t move according to your view.