Off the top of my head I don't really know. But then if you had asked me 20 years ago if we'd need multi core multi GHz multi GB computers to display a web page I'd probably have said no.

I suppose the os could reserve registers for itself to save swapping in and out quite so often.

Register windows for applications/functions/threads.

Or maybe something radically different, like get rid of the stack, and treat them conceptually like a list?