In 2022, the British government spent £3.5k ($4.4k) per person per year on healthcare. The US spent $13k per person per year in 2022, of which $6.2k was government (national+state+local)[2]. The UK government spends less per person than the US government on healthcare, even before the amount paid privately.
Even if you think the UK's healthcare is worse than the US (which I fundamentally disagree with), you have an extra $2k to play with and do better than the UK before it costs more than the current system to the government, and then another $6k of extra tax before people would be more out of pocket than with private healthcare.
Healthcare is complicated, all systems have flaws and all are vulnerable to being manipulated. None of that changes that the US has the worst system, run in the worst way, with the least efficiency. And that's without even getting to the obvious point that a country where people are healthier is worth paying for: my friends and family, colleagues, people I interact with being well, living longer, and not having diseases is very worth paying for and I want to be taxed to achieve that.
[1]: https://www.ons.gov.uk/peoplepopulationandcommunity/healthan... [2]: https://www.cms.gov/data-research/statistics-trends-and-repo...