It also, to the grandparent's point, would not really necessitate anyone spending anything differently. The amount employers pay to private healthcare plans instead becomes a corporate tax; the amount individuals pay to private healthcare plans instead becomes an individual tax. But just by dint of it all going to the same pool, which now covers everyone, gives such massive pricing power that all those "$64 for an aspirin" BS charges will be cut to be in line with, yeah, any other country.
Universal healthcare funded via taxes is the exact opposite of insurance. Insurance premiums are decided upon your medical profile and risk. Taxes are based upon income, which has nothing to do with health.