Sadly, it seems convincing. Thing is - I'm not opposed to a change in our system, having lived in and understood the system in France. Being UK we'll probably do it all wrong and it will be the worst of all worlds.
I would like to see a variant of the French system, where your N.I. pays all but a small percentage of your treatment and you take out a 'top-up' for the remaining 20%. (There is a list of serious diseases such as cancer, heart etc., which are covered 100% for all.)
It is a numbers game for the insurance companies and they cannot cherry-pick - you apply and pay and they must accept you. Where I take issue is the way that the price soars as you get past retirement age and your income decreases - of course I was on UK pension and French pensions are massively bigger. There is also an emergency system for those who cannot pay of course (but it is means tested).
Parents take out 'top-ups' for the children too.
You don't have to do this of course, and OH didn't so he just paid the extra bits as they arose.
Being us, it'll all go wrong. :(