My room is over-symmetric, but I have recorded in some more open, completely asymmetric space in the house and it's not a problem in recording so much as one in mixing. And, having *near*-field monitors is the primary tool used there, along with attacking the 1st reflection points on the sides with trapping (or really heavy drapes) and, possibly "clouds" (overhead panels).
The energy in the sound dissipates (inverse square law) with distance, so anything that gets past your ears is going to travel some distance before it returns. If it returns quickly, then it potentially confuses your mix decisions, especially if it hits highly reflective surfaces. That's why you trap 1st reflections and behind you. And, it's why the asymmetry is beneficial to some extent there, since it some reflections will effectively lose all their energy in that travel. Now, if you are recording a drum-kit or loud electric guitar amp, not so much, but for acoustic recordings, the energy is low, and you should mix with your speaker levels not too loud, either. I'm not discounting it as a factor, just saying I think you can probably control it, once you set up and get an idea of what it *might* be doing to your monitoring environment.
I have "Pergo" flooring with some cheap area rugs, and just trapping for monitoring overhead. I think it's Ok. (Should be some videos in my profile recorded in that room, and the recent mandolin duet to decide if I am full of mud or not.)