[mattmanser]

No, I replied and rapidly edited out a few words of my original reply to try and make it clearer, but seem to have done the opposite. The last sentence initially started with "Interestingly". My original meaning of the last paragraph was "here is an interesting, related, factoid. The UK happens to have a regressive tax to pay for the NHS".

My main point is that governments are free to provide the same service to rich and poor without that being regressive or disproportionately favouring the rich. For example, bin collection, policing, national defence, fire safety, etc.

A universal health service can simply be another collective service. If you want more because you're rich, in the UK we also have private healthcare services you can pay for, much like you can pay for a cleaner in addition to your bin collections or a body guard in addition to the police or national defence or pay to install fire suppression in addition to the national fire service.

What makes it regressive or not is how it is taxed for.