firstly: most VR apis are closed-source and thus gpl-incompatible. That said, there are a few options like OSVR that might be legal to use in quake.

secondly: I'm sure most maps/mods would be fine on a VR headset (take your normal framerate and halve it - if the result is below 144fps then it'll be terrible in vr).

thirdly: quake's fast motion combined with the lack of physical movement will make pretty much anyone who has ever been slightly motionsick to want to vomit (vr speedruns will thus be even more impressive...).
I get the impression that most VR-focused games are basically turret shooters as a result, and the rest are all slow-moving/non-action games.

fourthly: input issues. with a headset you can't see the physical stuff infront of you, so you probably don't want to have the user using a keyboard, so you end up with a gamepad and all the issues that come from those. And because the view will end up moving separately from the crosshair, you're probably going to be missing even more.

fifthly: someone will NEED to rewrite the hud, and all the menus if they're to be usable. Its no longer quake. :(

There are existing quake engines that have VR support in some form (although generally forks of DP), so if you've already got a headset then you should be able to see what the resulting gameplay is actually like, and how long you can play for, etc.

</opinionatedrant> 

All of your points are valid indeed. I must admit that several things would make Quake unplayable in a VR headset. Most probably I should forget that idea of a view of the Quake universe all around my head (but still, that would be awesome to feel to be in there for real!). 

"Man walks into a bar and says can I have 5 pints of VR?"

It's seriously not that easy to retrofit VR to an existing game. You can't just arbitrarily pick a game or game engine and expect VR to work with it. That's why engineers in VR companies earn oodles of money, you know. 

Is it really true that quake can't legally link to a closed source library? What about direct x, isn't that closed source?

I believe quake could still be quake with different menus and hud.

those points aside, i haven't had much experience playing vr games but rapidly looking around or moving fast did seem seem problematic for me when I tried it. Due to motion sickness mainly. Also the weight of the headset I tried made rapid head movements uncomfortable.

A quake mod with more focus on slow looking and careful shooting and less on quick movement and twitchy reaction might work though. 

Most OpenGL implementations are closed source too (hint:the "open" in OpenGL has nothing to do with "open source"),

The GPL does in fact have various library exceptions that do allow such linking, but many GPL zealots behave as though it mandates what they would like it to, rather than what it actually does.

Another problem with VR is that it's still quite fragmented, with no single open standard covering everything, nor even the equivalent of a Directx - a closed standard that nonetheless covers 90% of the market. 

https://youtu.be/gIQ2PdYJ5GQ

I've played this. It's been a while but it is a hoot to be inside your level in 3d. 

There's even an app for Google Cardboard. It costs a dollar and is a Darkplaces mod. If I had a cardboard headset, that would be the first thing I'd try out. The crosshair is centered to the players view and not the right stick. 

I have a Rift and it's amazing.

However Quake in VR is an absolute vomit-fest. 

Why? Could you elaborate a bit on this? Have you tried Quake with your helmet? 

played it few times with colored goggles in 3D 

I can't fully explain but some games can make you really motion sick.
The speed of Ranger in Quake is very fast and you're about 3 feet tall, so you're kind of zipping around at this weird height. The best games in VR have very little moving around, hence why locomotion in games tends to be very slow or using teleportation.