In my experience "free" healthcare stops being a thing once you get above certain income level as the service provided by the public healthcare facilities is subpar (waiting lists huge, best specialists often work at private clinics, etc.) so you end up going private but you still end up paying a huge chunk of your income in tax.
That's not true here in the UK. People do use private healthcare but they're in the minority and it's usually for expediency rather than quality. Many very rich people still get treatment on the NHS. It's very, very good.