The issue is that the only voices for a hybrid system are the voices that would probably actually dismantle the public system if they could, and the current system really does work pretty well when you have a serious illness. I think the public system could still keep a monopoly on those treatments though, but I think private could complement other areas where there isn't a reasonable cost-benefit for the government to cover but plenty of people are willing to pay for the peace of mind.

You could for example, have some properly regulated private option for people that want some level of additional preventive care like regular blood tests, yearly checkups or screenings. It is bizarre that we have thousands of naturopaths and chiropractors opening up private practices and charging market prices, but an actually trained non-quack GP isn't allowed to do so.