That's how public health works. It's the same as mortgage insurance in Brazil (where I come from), which is mandatory, and, since it's mandatory, it doesn't consider actuarial risk.
BTW, “right” and “wrong” are human constructs, so you are totally free to organise a society around the survival of the richest. It’s just not a society you’ll like living in.
There are other ways to properly fund universal healthcare that does not involve creating artificial taxes:
- Increase the actual income taxes.
- Policies that mandate the allocation of revenue from vice and environmental taxes (alcohol, smoking, gambling, fossil fuels) to the health system.
- Social security reform. Pensions should not be an investment, only insurance. Turn pensions into an UBI program that has a hard cap.
All in all, my point was only that the amount of taxes that people pay and quality of services are not necessarily related. Germany has high taxes and expensive-but-adequate healthcare. Greece has high taxes and expensive-and-inadequate healthcare. Switzerland has low taxes and universal/cheap healthcare (max. $5000/year deductible, max charge per hospitalization of $700).