1) I should've said the UK has a private tier for clarity.

You will get to see a private consultant a lot quicker, than the very same physician via NHS referral.

Quite literally you could wait months, or pay a few hundred and see the same exact person in a couple of days. In fact, when paying private - the private consultant himself will be treating you, vs. when on NHS - it will likely be his students/trainees that will be hands-on.

NHS hospitals are on a fixed budget, but of course cost controls means nothing - only putting patient interest first /s.

2) As for the insurance payouts - that was regarding systems where physicians bill on fee-per-service model, the most predominant setup in the US: https://www.ncbi.nlm.nih.gov/pubmed/20467910