I've always lived in the UK so have always had the NHS. I have blindly supported it entirely up until fairly recently. On paper, it's a great thing. However, there are some issues which have crept in which undermines the whole system and means that it's not quite as great as many people make it out to be.
1) It's not nationalised. It's increasingly private companies charging exorbitant fees which are simply paid by the taxpayer. This isn't just the healthcare itself. It's the maintenance of wards, the food, the cleaning etc. You can't change a light bulb, or fit a cabinet. It has to be a specific company who does it and they charge ridiculous call-out fees for simple tasks most members of staff could do.
2) Because it is paid for by taxpayers, innovations have to be 'public-friendly'. There's a PR element that is arguably much worse than that faced by private companies. Because the patient isn't paying, there's not much in the way of optional treatment and, say, signing a waiver to say you understand the risks because 'that's my dime you're not curing people instantly on'. You also end up with medical fads gaining popularity and then falling out of favour pretty rapidly.
3) There's a lot of talk about 'positive risk taking', but that's only on the front lines. They're shit-scared of being sued. You need a policy for every little thing and so that means a lot of e-learning for staff which is so tedious it gets skimmed and so the staff aren't really getting trained properly at all. Even the basic CPR course is passed by people who clearly were not doing it properly in the in-person training sessions.
The safety net is fantastic and I'm glad we have it because I have needed it and the effects of stress on health, especially dwindling health, is no joke. However, the pricing structures are the main problem in that medical treatment is way too expensive - unethically so, whether private or public. That seems to break both systems.