It’s not ‘the rich’ paying in that case. It’s ‘the majority’.
My point is, healthcare is being funded by everybody who works (also everybody who consumes, as you have to pay VAT) not only the rich.
This becomes even more pronounced if you take into account who is using the health care system as low income tends to be tied with bad health (diabetes, smoking related issues, hard physical labour, etc).
Note that I'm not saying this is wrong. Broadest shoulders should bear the largest burdens.