In the UK there are ways to scam the system so you can get a boob job or a sex change type of thing. Any prescription is heavily subsidized so the boner pills are covered. Actually they might be available over the counter (generic) now. The NHS is painfully slow in some areas and some folks use insurance (BUPA) to get treatment quicker.
Cosmetic surgery can be a bit tricky to get on the NHS but is available depending what it is. I know two people who managed to get it but it was a struggle. One was to get their nose done, it was ever so slightly misshapen and the other was to have a mole removed from their nose.
Generally it is allowed if a psychologist (or other specialist) believes that not having it would cause issues. If it's just something the patient would like, but won't suffer without, then they have to pay for it themselves. If your breasts are so large that they cause back pain, breast reduction surgery would be covered; If they are significantly different sizes, and this causes distress, then a boob job might be covered; If you want big tits so you can get a modeling job, then you have to pay for them yourself.
The system is based on medical specialist opinions of patient welfare considerations. Unlike the US system, where it is based on what the insurer can get away with not covering based on the small print in your contract.
Your view of the US system is not quite correct, although I have encountered insurance companies who did do their best to not pay any claim and indeed, which made a practice of denying all claims the first 2 or 3 times they are submitted because some percentage of providers and some percentage of patients will simply give up and pay the claim. Never mind that the repeated filings, repeated requests for the same documentation of necessity over and over, the requirement that physicians personally sign all claim submissions, etc. serves to drive up the costs of coverage for ALL patients.
Unfortunately, those unethical insurers tend to be the ones most 'affordable' to low income people or their employers, while providing as little coverage as possible. But most insurers that I have encountered are more ethical than that and work to pay claims as efficiently as possible.
I was curious as I have known patients in the US who have had various procedures that some might not consider to be 'medically necessary,' including medication for ED, breast reduction, breast reconstruction after cancer, etc. I didn't know how those issues were handled in single payer universal health care systems.
Asking as a purely hypothetical: How do you feel about those who are better off financially being able to purchase private insurance which supplements their government issued insurance?
In the US, one of the big issues is that there are gross inequities in the kinds of care people can afford based on income. My husband and I are fortunate in that we each have very good insurance coverage and for a modest sum are able to cover our spouse as well, which has translated into minimal medical bills even after say, surgery for cancer or cataracts or hernia repair. We have good dental coverage (have not had to test the coverage for dentures or implants yet, thankfully) and can get the cost of prescription eye wear reimbursed via funds provided by our employers. The sad irony is that our offspring, young adults new in their careers (and earning far less than their parents), pay more out of pocket for their insurance premiums than either of their parents and would pay more out of pocket for routine care, or for say, a hernia repair which can be needed at any age, not just middle aged to older adults. We can afford to pay out of pocket of a couple of thousand dollars which thankfully, we have not had to do. For my offspring at this stage in their lives? This would be very difficult for them to do. One of my kids had a serious case of the flu and had to go to urgent care, get meds, etc. Was outraged at the cost of the care but this particular strain was claiming the lives of otherwise healthy young adults so it was necessary. But that few hundred bucks was a lot out of their budget, especially since while ill, they weren't earning money either. Which is not uncommon and is grossly unfair. And frankly often results in providers not getting paid, courts, etc.
My absolute belief is that EVERYONE deserves the level and access of care that my husband and I enjoy. Or better. Everyone. I don't care if you are wealthy or poor, an addict, a health enthusiast, young, old, etc.
There are other stark inequalities as well: people in rural areas have more difficulty accessing health care because there are proportionally fewer health care providers. This problem is increasing as smaller hospitals consolidate/close. In low income urban areas there are fewer providers as well, at least partially because Medicaid (govt. insurance for poor people) pays less than it costs to provide the services needed. Increasingly, Medicare (govt. coverage for those 65+) does not cover the costs of providing services. And frankly, insurance companies are looking more and more to Medicare and saying: If Medicare only pays $75 for this, why should we pay more? I see the point but also see how providers are working very hard to become more and more efficient, to reduce costs. There is a really genuine fear that this trend will decrease the number of people wishing to become physicians if they are not able to earn enough to repay medical school loans and to raise a family in a decent middle class level.
Another real concerns about single payer health insurance in the US is that such coverage could/would be subject to the political fake religious views of legislators. See outcry at covering women's birth control or even pregnancy and labor and delivery as a mandatory benefit. Of course, wealthier people will always be able to find a way to get whatever medical care they want. This also plays out in end of life care. Both my husband and I lost parents after long illnesses and each of us had one parent who, sadly, spent the end of their lives in a skilled nursing home facility, in separate states. Both states are pretty conservative. However, there were stark differences. In the case of my parent, morphine was offered to alleviate pain, although it would (and did) suppress respiration and in a small way, probably hastened the inevitable death of my parent. But my parent died without being in pain. My husband's parent, in a different state, was not offered enough pain relief to make last months bearable. Unfortunately, and predictably, this had a serious negative impact on relationships with family and friends and caretakers. We were all miserable, not just sad.
In the US, there is a tremendous push by (some) patients to do 'everything possible' to extend the life of a terminally ill patient, rather than provide palliative care to support patient (and family) through a final illness. This also adds greatly to the cost of care in the US. Within families, there can be conflict. There was in my family but fortunately, more rational heads, and the progress of my parent's illness prevailed and they were spared useless, expensive, intrusive, uncomfortable treatment while being kept comfortably pain free.