I would argue that dedicating a larger part of a nation's output to healthcare is not bad in itself. In fact the better futures I can imagine all have very significantly broader healthcare provision. And we'd be spending more on health because we can.

Efficiency matters, of course, and a higher fraction of GDP spent on healthcare isn't per se better, either.

One problem with private provision of anything is that a company only cares about the revenue it can actually capture itself. Nationalised provision, using tax as a revenue stream, can look at whether something is beneficial on the whole even if it isn't directly paid for.