I agree with almost everything you've written. The NHS is indeed treated like a sacred cow, and it is absolutely not world beating. I live in Switzerland, but am British, and I would infinitely prefer to get my medical care here and to pay for it. The French medical system has a better reputation than ours also.
Swiss medical insurance is actually quite strongly regulated and not like the US system at all. Extras are generally where insurance make money, like having a private room in a hospital instead of a ward.
Where I disagree is that a change of government will improve things, because I don't think 'more money' will magically solve all of the problems. As an example, GPs should be doing face to face appointments again as you say, and they should be on call for out of hours. Not for extra money, they're already highly paid. This is just part of the job - people aren't ill conveniently between 9-5 Mon-Fri. Before anyone says this is unfair, UK software engineer salaries look nothing like US ones most of the time, whereas doctors are 'raking it in'. Yes, being a doctor is a tough profession, undoubtedly, but getting into medical school is highly competitive and sought after. So you either want the status and money in exchange for unsocial hours and dealing with the sick and dying or you choose a different career.
I don't find it a convincing argument that 'this is all the fault of the tories' because I also had a problem with panic attacks when I lived in the UK under a labour government, and was also outright refused treatment because our local area had only adult facilities and I was 17.5 when it started. I've plenty of other stories, but this is mine.
Generally UK politics is polarised like the US and people who believe the conservatives' sole motive in life is to dance on the graves of the poor while watching a food bank burn are likely to be overrepresented online. Remember that austerity came on the heels of Gordon Brown trying to spend his way out of a recession, the same PM who as chancellor sold off the UK gold reserves at the bottom of gold value and tax raided a bunch of pensions. Labour are by no means perfect either, and unfortunately even governments have to budget.
Don't get me wrong, the tories have been the government for quite a while now. They've had time to improve things and they definitely haven't. I'm just saying the idea Labour will magically resolve NHS issues is a fallacy. I'd argue that the real issue is the short term/electoral driven policymaking with regards to the NHS - it is a sacred cow, and even the slightest mention of change could potentially be political suicide.