Don't you have private healthcare in the UK too, if you aren't satisfied with the NHS?
IMO universal healthcare is awesome as the final safety-net that provides critical care, no matter your financial or employment situation. Yet it doesn't need be the only option. If businesses or people with money want to pay more to get care faster from private sector, that's okay too. It's how the system works here in Finland.
Ditto Australia, hybrid public / private healthcare ...
* private is good for better rooms, more scenic views, personalised spa like service and near immediate access to non life essential procedures
* public keeps the majority of people alive and triages procedures, you can get overnight heart stent surgery for free if required, might have to wait a few months for non critical knee surgery.