Ok, so you're suggesting always running the browser in a VM, and using the GPU from within the VM (via the host OS of course).
I believe significant work has been done on the browser/graphics sandboxing problem. Whether browsers use techniques comparable to virtualisation, I don't know. I'm afraid I don't know much about how that's done, or how effectively virtualisation is able to contain the operations of VMs, or how high the performance penalty is.
Going with guesswork though, it seems to me virtualisation doesn't offer particularly solid guarantees here. If the host OS has a buggy graphics driver, it would presumably be possible for it to leak data back to the VM. Any facilities the GPU can offer to help contain semi-trusted graphics contexts, should presumably be available for use directly by the browsers, without running a guest OS in virtualisation.