Hot-take: It's an emotional defence mechanism: on-the-whole the UK and US are far too similar and integrated that it's natural for middle-class Brits to larely consider themselves peers, and not near-peers, of their US counterparts - so when you have that view of yourself and your place in the world but then look at the stark the income disparity, you're going to comfort yourself with all of the bad things about the US (and the US' bad things are legion) - and invoking the egalitarian NHS happens because the UK gets its impression of the US healthcare "system" (industry?) from things like Michael Moore's
Sicko or Times columnists reporting on all the messed-up healthcare injustices that happen in the US - but there is a very real ignorance of what healthcare is like in the US when the system does actually work well for you.
And if it isn't NHS vs. "doesn't &everyone* get medical-bankruptcy?" then it'll be about guns, or the death penalty, or overt racism in the south, or corporate america's excesses, or US foreign-policy, and so on. Because those are the things that Channel 4 will report on - but you won't see or read stories that upset anyone's feelings on their place in the world: and it works on everyone: I've already mentioned Guardian-reading types, but also and especially the Brexit-types: who still desperately want to believe the British empire could be brought-back because the Daily Express told them so.