You took a false dichotomy and jumped to an absurd conclusion. It makes you seem more concerned about an ideological position than thinking the problem through.
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.
- Supplemental and voluntary insurance plans to work on top of the existing public network. This might be risky as it can introduce a dual-class system, but (a) it's already the reality in most countries anyway and (b) could be avoided if the system is built around a "cafe sopezzo" [0] mechanism (the priority is given to you when you use the service, but redirected to non-paying members for the months when you don't)