On the NHS, I tried for years to push for improvements to switch to digital cancer screening invitations after they missed my mother (offering to build the software for free), which is now happening, but suggesting the NHS isn't perfect is against the religion here. My sister who works in NHS DEI hasn't spoken to me since publishing a book on it.
Every time someone with the finances, vision and ability leaves I think the situation gets a little bit worse, it increases the proportion of people remaining willing to put up with all of it. Anecdotally, many of my friends have already left, some of the older generation want to leave but feel tied in. My flight out is in 6 weeks. Good riddance, no doubt.
I don't know anyone that doesn't complain about the state of the NHS. The only time I've heard anyone defending it would be when compared to countries without national healthcare (e.g. America).
A lot of that money has gone on stealth privatisation through inefficient outsourcing of contract staff and PFI of infrastructure.
So the actual standard of care is far lower than the funding suggests. And it has been deliberately run down so a US-style system can be implemented.
So yes, the organisation should be improved, but in the exact opposite direction to the one you're suggesting.
The UK's real problem is that it's run by an out-of-touch inbred aristocracy with vast inherited wealth, working through a political system which prioritises stealth corruption over public service.
They don't see why they should contribute anything to the welfare of the peasants. The obligation is all one way - from the peasants to the gentry.
And there's a layer of middle class professionals who have convinced themselves they're the gentry, even though they can't afford to pay their school fees, never mind maintain a huge estate.
So - private ownership good, public spending bad. More sensible countries don't have this attitude problem, and are proud their public services actually benefit the public.
So public/NHS vs private/US system is a false dichotomy, and "free at the point of use" is a red herring.
Looking at the reactions, this whole threads does exemplifies what the OP said about the NHS being a "religion".