IIRC in the UK - for decades the self-employed were allowed to opt-out of the NHS and paid physicians and hospitals from private funds. Health Insurance was not a huge market.
From Wiki: According to the World Health Organization, government funding covered 86% of overall health care expenditures in the UK as of 2004, with private expenditures covering the remaining 14%.
Apparently, the NHS is so thoroughly entrenched - physicians are critical of the private plans as being ‘too restrictive’.
all it take is from a few “rebel” docs to make money and improve service for tidal wave to occur. The docs are probably touting the “party line”.