Do you have some source that universal health care would reduce costs? I think it would be just extra tax, and medical expenses would just increase proportional

Do you have some source that universal health care would reduce costs? I think it would be just extra tax, and medical expenses would just increase proportionally, similar way as with student loans. My country has nationalised healthcare, yet you still have to pay for private doctors. There are no state dentists or pediatricians. And waiting list for surgery is months or years.