That seems like a strawman. Upthread you were pretty clearly arguing from a libertarian perspective (I genuinely thought that your "only NHS" quip was humor, not that you were being literal -- the article obviously doesn't say that at all).
Now you're saying I'm wrong because there are other socialized forms than NHS that work too. Well, OK! I submit. Use one of those.
* Medicare in the US (single-payer, private providers)
* Medicare Advantage in the US (government provides capitated payments to competing private companies, which then do all the administration work)
* The Singaporean system (complicated, but revolves around mandatory payments to HSAs)
etc.