To be mildly flippant: Head rotation works perfectly fine when on foot; You can look around freely in the space holding the virtual screen which displays the game in a mono projection.
That is not the problem. -The problem is that there should be no virtual 2D screen in the first place; You should have the stereo camera pair directly in-game, just like you have when you switch to external camera mode. You could lock the position of the virtual screen to the camera, so that it is always right in front, and map the mono game camera rotation to your IRL head rotating, but that would still be a virtual 2D screen - you'd still be looking with one eye closed, through a mail slot, even though you could now swivel and tilt the letter box you are trapped inside.
Making the view VR would involve a few things (in addition to incorporating head rotation input to the game camera)...
Heads-up display UI elements (mimicking in-game holographic displays) would need to be arranged in 3D space, so that they are positioned for comfortable reading within your field of view, which is larger than what we're given with the virtual screen. This includes making the aiming reticle draw with the same amount of stereo separation as the target, as if it was the same distance away from you - again for comfort -- preferrably so should "speech bubble" AR markers that attach to objects, such as floating NPC name tags, and interaction guides. This is all simple enough if the HUD is "properly" done, as textures mapped to meshes in 3D space -- less so if it is all 2D, drawn in screen buffer space.
After that, most things could be seen as optional, in the short term... E.g: For things to look right, on top of just being playable, you'd want to use the third person version of your player character's model and animation set - not the disembodied hands floating in some odd place to make them peek up from below the bottom of a static screen version used for monitor play (the model already looks up and down when you aim with mouse/stick, so that should work inherently right off the bat, after adding head rotation input, for the benefit of other players seeing you). You'd want to draw the inside of your helmet, where similarly to the above, the current effects with condensation on the inside of- and reflections/refractions in- the visor could be a 2D overlay, which looks kind of wierd already when playing on monitor, but this could either be accepted-for-now, or simply turned off, and you could just skip rendering the head and helmet both, like is already the case in-vehicle.