What "Rationing by price" actually means is making it unavailable to people who can't afford it. You only have to look at other situations where people with the lowest incomes are subsidised to know that there will be those that don't meet the threshold for help but will still struggle to find the money.
I don't understand the blind faith in private companies providing a better service. It hasn't worked too well with rail, utilities, mail, dentistry and so on. My NHS dentist has just dumped all their NHS patients and now there are no NHS dentists available locally. So that really isn't working at all. I'm struggling to think of any service that has been improved by privatisation.
There are a lot of issues with the NHS and it is not just about throwing more money at it. There is a complete lack of joined-up thinking. Social care (oh yes, private companies again) is a complete disaster. It's having a huge impact on the NHS. We are still paying for those people to be cared for, it's just that the money is being spent in hospitals instead of in care homes. The nationalised service is picking up the pieces for the failing private sector service. I don't know (and I may be wrong) but I'd hazard a guess that occupying a bed in a hospital is more expensive than occupying a bed in a care home or providing at-home care. So not funding the social care system properly is, I suspect, costing us more money than it would cost to fund it properly in the first place.
The internal market in the NHS causes issues too. One department makes savings by cutting services only to cause more problems for those patients down the line that end up costing far more for another department (or the benefits system when they can't work). For example, the amount of gatekeeping on referrals for assessment for ASD/ADHD etc means that people are going undiagnosed and unsupported leading to mental health crises further down the line. That's only one example, there are plenty of others.
Private healthcare providers shouldn't be able to just dump patients back onto the NHS to deal with when things go wrong. They should have to pay something if they do.
I think we need to sort out the social care system as a top priority. We need to address the fact that 10% of NHS posts are vacant. There is something horribly wrong to have that much of a staff shortage. Again, I don't think that is just about money either but it probably doesn't help if people can earn more in less stressful jobs. If we don't get these two things sorted out ASAP then I don't see how things can improve. In the longer term, we need a more preventative approach. It's less expensive to stop people from getting ill than it is to deal with the illness,
I have a (not imaginary) DC with multiple chronic health conditions who should be seeing a consultant and having health screening tests every 3 months. So far the appointments have been 5 months apart (so there have been 2 in the time there should have been 4). It's coming up to 5 months again now and we haven't received a new appointment yet. It's not ok. Something has to change. I just don't think the private sector offers a magic wand.
Ultimately, healthcare has to be paid for, and we are going to pay for it. The question is do we want people to pay for what they use (regardless of being able to afford it) or do we want people to pay in what they can afford to pay so that everyone can have the healthcare that they need? Adding in people paying a nominal charge at the point of use probably won't gain much, if anything, by the time the cost of administering it is taken into account.
It's also important to understand that there is a cost to not looking after the nation's health. People who are not working, of whom a sizable number are ill, need financial support and may need looking after most often meaning a family member not working so that they can care for them. So then that's two people not working and needing financial support. The economics of a country are not the same as those of a household. As a country, investing in some areas means savings in others and potentially an increase in tax income. It's not just a question of having to find more money.
Sorry, that was a bit of an epic.