Maybe, I am a little biased, having worked for 40 years for the NHS, but I prefer a system which treats according to need and not whether the insurance company is prepared to cover.
I believe that the proportion of the NI that is used for the NHS is less than the US insurance contributions. It also covers social care, statutory sick pay and state pensions, As I am retired, I no longer pay NI anyway.
Yes, of course we all pay towards everyone’s care, not just our own, but that is true of any insurance policy. I have (so far) never had to use my house or contents insurance but I know it is there if I need it. I also know there are people who have had to use it several times. I don’t resent that because the time could come when I do need it.
Because I have worked for the NHS, I am aware, perhaps more than some others, that there is plenty of room for improvement in the NHS administration. Until that happens, I am happy to rely on it for my care. I have had to use it twice for my care since I retired, once for a knee replacement and once for injuries sustained in a fall. I have had surgery, nursing care, X-rays, MRI scans, emergency paramedic care (in the latter case), physio, hydrotherapy, out-patients appointments— the list goes on. All I had to shell out were taxi fares, until I was able to drive myself again, petrol and car-parking.
Incidentally, at my local hospital, parking was only brought in originally to discourage the public from using the car park while they commuted for work leaving no space for patients or staff. It went towards paying for parking attendants too.