Planetary Annihilation 2 in VR?

Battle chess would be a different matter, as the control surface (the chess board) is already a plane, so you can just project the actual chess pieces in 3D on top of it. For an RTS with a purely flat map (respectively when the unit movement is solely restricted to that), that would work just as well.

As for the added value - not much. At least not in direct comparison to generic touch controls on a sufficiently large screen. The main improvement would be from the touch gestures, not from the display technique. The VR solution simply provides a more cost efficient approach, compared to the cost of a real large scale touchscreen.

I feel like it'd be easier to just cut out the hard part entirely -- controlling the units. The players need a lot of information from the GUI, and the GUI makes things easy for them. The freecam is never used by players, and I don't see them using a VR mode either, but who does use the freecam? Spectators.

The ability to select which planet you want to teleport to via a radial wheel + the ability to scale up or scale down, and "drag" the earth Google Earth VR style would be enough, I feel. You'd probably want statistics, so you could attach that to the radial menu as well. I don't know if nested radial menus are a good idea, as I've only seen a few VR games and I don't own a headset myself, but that might help keep things organized.

All you need to nail is what people already use spectator mode for. They use it to overview battles and look at statistics. Those statistics need to be easily reachable, no matter where you are (radial menu). The world needs to be capable of scaling such that you can make small engagements seem bigger by just zooming in (scaling up/scaling down). The world needs to be able to be traversed quickly (spin the planet around with your hands and zoom in where necessary, Google Earth VR style, where the planet is either in front of you or below you). And of course, you need to be able to get the big picture, meaning you have to be able to zoom out to see all of the planets and orbital action going on.

The game is mostly about scale, so being able to scale up and down seamlessly is key. Your scale determines whether you're admiring a battle from a first-person perspective, overviewing a small area, looking out over the ocean, zooming by a landscape, inspecting units on the orbital layer, viewing the orbital layer from underneath, viewing it from above, scaling out and looking at the players bases, examining the solar system, seeing out from a unit's perspective like you're in the cockpit, and so much more. That, I feel is the hardest part of PAVR.

Again, I think Google Earth VR is an amazing example of how this can be done. I think designing a system closely resembling that would be the first step to making something like this.