If your universal health care system is some variant of "single payer", which is what I think is proposed here, then the fact that it is really expensive is lar

If your universal health care system is some variant of "single payer", which is what I think is proposed here, then the fact that it is really expensive is largely irrelevant, and for a really obvious reason: You may be paying a lot of money for government funded health insurance, but you are not paying all that money to a private health insurer like you are now. Essentially you are just writing a check to the government rather than a private company.