I would be _ecstatic_ to give up half of my salary for such a system which assures that irrespective of my employment/financial status, age or health, I'll get the care I need, until I die.
For example you can find German news articles about how public insurance doesn't cover some tests that confirm/deny if you have some life threatning condition or not, even if you have all the symptoms and the doctors says that's the next step - while private insurance does cover additional tests.
And private health insurance is only available to individuals earning well above the average German salary.
I am in the UK, we don't get medicine for some things because it is too expensive: HRT has been in shortage for years, we don't get most newer cancer drugs (it is unrelated to efficacy, it is just too expensive to treat people), epilepsy drugs are the same. Because drug prices here are so low, pharmacies get drugs, and then ship them to Europe to flip. I have relatives who are sick and don't get treated because it is NHS policy not to treat conditions properly (the most well-known one is CFS, the UK's approach to CFS/ME is...unique, and governed heavily by cost). And ofc, lots of money thrown into "cheaper interventions" like public health advertising (coincidentally, the people who run these campaigns are friends with people in the NHS...which is nice for them). Mental health is another area: too expensive, massive underinvestment, even today most of the mental health system is nurses who get a couple of weeks training from psychologists, psychologists are too expensive (somehow, almost no-one who studies psychology in the UK ends up doing clinical work).
There is no trade-off. Someone has to pay because doctors don't work for free. The US has a relatively optimal system with targeted universal healthcare that is heavily subsidised by the wealthy. Germany is a derivative of that system with a relatively large private component that subsidises the rest of the system. It is far better to overproduce healthcare for the wealthy, then underproduce it for everyone else. Ofc, "free healthcare" sounds very nice (unless doctors start working for free, the cost of a US public health system would largely be what it is already...Medicare and Medicaid is cheaper...but not by much because doctor and nurses, for one, are relatively well paid...in the UK, nurses make the equivalent of $25k, again no trade-offs).
My feeling is the NHS is a good institution in an unfortunate political culture. The UK is an essentially conservative state (they have been the ruling party for the vast majority of the last century) which is a poor fit for a pretty radical socialist healthcare system.
Also, the NHS is one of the only things on which there is almost no real political debate in the UK. The BMA is probably the most powerful lobbying group in British politics (and this isn't good, they are one of the more sources of stasis, they have opposed every change in health policy...they also opposed the introduction of the NHS). So the problem is the opposite: if anyone tries to reform the NHS is any way then the political opposition is instant (and the only way someone like Blair did reform at the edges, was to pay off doctors...which ended up costing massive amounts of money and leaving the system in a bigger hole). The main conservative force is the NHS itself...it isn't really radical, it is just a system that doesn't really work but Brits have this weird tribalism built up by tabloids telling people that someone is trying to privatize it (and btw, this is the conclusion of anyone with a brain...the NHS doesn't work well, the wealthy and middle-class need to subsidise the system more heavily but people want a Nordic size state with US taxes...and btw, what people don't understand is that we have US taxes with a public health system that is half the size of the US public health system...so we don't even do that properly). I also wouldn't call it "socialist" either, there is no real subsidy, US healthcare is way more redistributive, it is universal but lots of other healthcare systems in Europe achieve universality with large private systems...so universality really isn't the dealbreaker that people in the US think it is. But most people are die-hard NHS supporters, so it clearly isn't "socialist".
Sajid Javid literally reads The Fountainhead twice a year - and he's not much more neoliberal than his predecessors.
My feeling is it's hard to succeed as an organization when your boss really would like your organization to fail so the free market can step in. And that's been the NHS's situation for most of its history.
Nonetheless, there are inherent inefficiencies of private healthcare, even subsidized private healthcare, in that it results in horrific paperwork multiplication and information siloing. In germany, where I live, the amount of paperwork you need to get insurance is insane. There are literally offices full of people in every city doing basically senseless work just to make sure people don't get more healthcare than what they paid for. It's also a strong reason why the UK had such an easy time doing a vaccine rollout - the NHS could just send everybody who was in x age a letter. They also pay far less for medication, because the negotiating position is much stronger.
Sure, you can't get a homeopathic suppository from your heilpraktiker, or give birth in a giant bath that's shaped like a vagina, but it delivers a good service for a low price.
The view that the NHS is being stitched up is another common conspiracy theory that is "common knowledge" and totally wrong. The NHS (and the BMA, particularly) have been given all the rope needed to hang themselves. Attributing malice to incompetence is at the root of most conspiracy theories.
An inefficient system that achieves patient outcomes that are many times better than the UK. I would take that any day. It is great to sit in a country that can provide good healthcare and marvel at ideological purity (it isn't ideological purity, it is conservative/reactionary thinking that drives everything in the NHS)...it is less great to actually be in that country, and be sick and not get treated. The UK achieves good outcomes given the cost...but that cost is very low and the outcomes are also very low (the UK's healthcare system is more comparable with middle-income countries, we are nowhere near most developed countries...and nowhere close to a top rank country like Germany). And btw, the UK is massively inefficient...we overpay massively for doctors (our wages are roughly equal to Germany), there are reams of middle managers in the NHS, any system will have inefficiency (and it is far more dangerous to have inefficiency in a system that isn't redistributive like the UK because it is largely poor people who pay for it).
And no, it isn't about insufficient homeopathy. I don't think people who have healthcare understand what it is like to have none. I am sick right now, I don't get treatment (in one case, the waiting list is too long, and in the other the cost is too high for the NHS to treat people). Most of my relatives that are sick, have either had bad treatment at one point that has almost resulted in death (in one case, multiple times) or don't get treatment for anything but basic illness (and then it is usually bad: for example, doctors will prescribe insulin for overweight people with type 2 diabetes because actually getting people to lose weight is too expensive...the UK also loves "public health" programmes because they are cheap, they don't work either but they are cheap). You call up for emergency treatment, you will wait 6-12 hours for help, and when you get taken to a hospital you can wait as long as a day to be admitted (most stats that are reported on this are fake, the hospital local to me has always hit their four hour target, I have waited in their four hours when it has been totally empty...it was recently discovered that all their stats were being faked by management). If I need to speak to my GP, there is so much demand that I need to call at 8 in the morning, by half 8 there are no more slots. If I do call at 8 then I will be triaged by someone with no medical training, and likely told that I can't speak to anyone. If you do go to a GP, you likely won't get referred to a specialist if the cost is too high (a big category here is mental health, people usually come into the system only once they attempt to kill themselves/have a psychotic episode/etc.). If you do get referred, you will likely be waiting months or years. If you need medicine, it will be low-cost and anything complex is either not available at all or is sold into markets like Germany with higher drug prices by UK pharmacies (for example, most cancer drugs aren't available...it is why the UK has the worst stats on cancer treatment in the developed world, by far...same for epilepsy). And the vast majority of GPs are exceptionally bad at their job. I have moved around the UK, I have had maybe 10-25 GPs, most are clueless...as an example, I know someone who had a stroke, and the GP wouldn't refer to a stroke clinic (and btw, because obesity/strokes are so common, they just give you drugs because everything else is too expensive). I don't actually know anyone who has had a high level of contact with the NHS who has a positive opinion of the level of care (this includes people working for the NHS too btw, the support that people have is mostly theoretical...until they get sick, and realise how bad it is).
I am aware of the meme about German doctors. But what you don't see is that waste is a sign that things are working (and btw, the UK still wastes more than anyone, I am in favour of wasting money on doctors...if the outcomes are there, but they aren't and nurses get paid starvation wages because of this overspend). If you attempt to reduce all waste in healthcare, people die. It isn't like other things.
Source: me, capable of going private insurance but it’s a complete waste of money.