I think it's time somebody asked the question. And it's not an easy one.
My take on this is that anything outside A&E can't really be a "common good".
You could argue that care for chronic (i.e., long-term) illnesses should be nationalised because of the potential of financially ruinous bills. I wouldn't argue that, but it could be argued.
So, would you support the NHS providing for chronic illnesses and what else would you want the state to provide in healthcare? (Or not, as the case might be!)