I wouldn't mind if the NHS got some extra funding, but only after the admin system and trust/market aspects were simplified.
I think a healthcare system like france has, would probably deliver better outcomes, but whether we have too many health and social problems now etc.. to adjust to a new way of doing things. The fact someone can have an accident, and call an ambulance and be taken to A&E [free at the point of use] and be saved is a great thing/concept, but the rest needs strong reform.
I remember going for an MRI scan, paid for by the NHS, in a private but separate clinic on the nhs hospital grounds, it was immaculate and well run, totally different to my experience of the outpatients dept. Must come down to the management I feel, and capacity needs building up once more.
Does seem to be a lot of errors happening like your family examples, perhaps because they're rushing and worrying about these targets? The last time I went for something they'd made a mistake with the appointment, and just cancelled it so was a wasted journey, and the staff at the reception desk always seem to struggle with the appointment system, lots of confused peering at the computer trying to work out what they need to press.
Seen some pics of nurses on twitter tonight, they really look like they've been at the coalface, they are doing a very difficult job wearing masks and PPE for hours. I feel Covid has caught us out more than countries like Germany, and exposed the issues the NHS has [the poor management and systems]
I wonder if we went back to look at the NHS in the 1950s, which I consider a bit of a heyday with matrons

whether they set targets etc..or did things a different way ?