I would suggest the bureaucracy required for means testing might cost you more than saved from not treating higher earners on the NHS....
I understand that One reason Scotland has free prescriptions for all is that (from memory) c. 90% had them free (older people, children low wage) anyway and the extra admin for the 10% would have significantly reduced the marginal saving. As others have mentioned, it's not like most high earners are not contributing significantly via income tax in any case.
It's a regrettable trend that a desire for "fairness" can often drive significant counter-productive complexity. (Some people even suggested that the energy price help should have been means tested which would have slowed everything massively.)