Ok fine I didn't realise you were trying to lay a couple of little heffalump traps, so instead I just answered what I thought made sense. The given analogies are clumsy and don't really fit ("run farms" is silly - the NHS doesn't produce all of the things involved in the provision of healthcare - medicines and such) but I will humour you and answer in the context of the UK:
> Should Government run farms and give you food for free?
Probably not, the existing system works ok enough. They can maybe help the poor a bit more so they're not dependent on food banks (free school lunches was a recent controversy that shouldn't have been)
> Should government build homes and issue them to people?
I answered and you didn't like this but - yes and they should build more. I'll give you a little bonus and answer what you wanted to ask - "Should the government be the sole central authority providing housing?". Probably not, the housing market works ok enough in general. However they can maybe help the poor a bit more by building more council housing, not doing so is has directly contributed to making housing unaffordable for many.
And to bring us back to the original topic:
> Should the government have setup a national healthcare system back in 1948?
Yes - in the wake of WW2 there was no existing, competitive alternative that served the needs of providing quality, affordable healthcare to the populace. The NHS went on to deliver and then some. Plus with ~70 years of hindsight we see that in spite of a decade+ of brutal austerity, the NHS still costs less and delivers better outcomes than privatised systems like the USA has. It was the right thing to do, it is the right thing to do.
Also you seem to think they’ve shut out private providers altogether. This isn’t true, private healthcare exists if you want quicker access to some elective or non-urgent procedures or treatments.
Re your final point - this is very interesting. I'd like to know what countries you think I'm talking about, and if your libertarian (I think I'm right in saying this?), small government setup is anywhere close to implemented somewher right now or if it's purely theoretical/fantasy.