If quality health care is in limited supply, with unlimited demand, what is wrong with it being reserved for?

If the tax system works, universal health care CAN be achieved, so why not help everyone who is ill, not everyone who is lucky enough to pay for it? There's not unlimited demand, and there's a way of ensuring that the supply meets demand. That's the way i'd run a country, because the other way leaves sick people who can be helped, not getting helped.