I live in Scotland, less densely populated than South of the border. Getting a GP appointment is... awkward. Unless I'm dead or dying I tend to turn up at 5 to 8 and speak to the receptionists, amongst the ringing phones.
Over my life I've had several operations after speaking to the frankly awesome staff from initial GP to Consultants/specialists.
The NHS has always been there when I have needed it.
Now, devil's advocate: I think it would have been a different story if I had lived in bigger cities such as London or Birmingham. Even Glasgow or Edinburgh. So many more people requiring the same service.
Now let's imagine I live in the USA.
"Envy of the world"
Yes, very much so.