> There is still out-of-network healthcare in many countries with universal healthcare

Can you provide links?

I've personally used the healthcare systems in Australia and Canada for two decades each, and also for a short time in the UK. I've never heard of this.

There is a small handful of clinics in Japan that do not accept the universal health insurance, such as specialist ones targeting English-speaking expats.

Example: https://www.nmclinic.net/index.html#about

BUPA is the largest private healthcare provider in the UK: https://www.bupa.co.uk/

The treatment provided will be similar to the NHS, but with less waiting (if relevant) and nicer facilities, such as private rooms rather than shared wards in hospital.

Link: https://www.reginamaria.ro/ - one of the biggest networks in the country. I have to use it for most of the regular stuff and I pay a subscription plus out of pocket for some consultations. This is on top of paying 10% of my gross income to socialized healthcare money stealing scheme.