I don't see the problem with having to have private insurance if you don't work and contribute financially to the system of the country in which you live.
I lived in Germany for about 8 years from 2000 onwards and my dp had to prove that he could afford to support me financially and I had to prove that I'd taken out private health insurance.
I was told that if I worked for 12 months continuously I would then be eligible for cover under their 'nhs' system.
I believe that this is a fair way of doing it and if it applied in Germany then it should apply for those coming to live in the UK.
When we later moved to the UK my dp wasn't entitled to claim any benefits, including NHS and all healthcare, until he'd been working continuously for 12 months (same as it was in Germany for me). We had private insurance for that time.
I agree with this system and don't see the problem with it. I think it's fair and should be used to clamp down on health tourism.
In Germany we had to show our health insurance cards at every appointment/ hospital visit/dental appointment, etc before treatment was given. My dp's was provided by the government as he qualified for their 'nhs' and mine was my private insurance card, which was my proof of entitlement. I actually think that they should implement such a system in the UK.