I don't believe it would, either more cheaply or efficiently.
You're arguing against economics there bro... Are you saying that central planning is more efficient in general? Or is there something special about those services which means a free market can't deliver?
How so, bro? I find it ironic that the only people who usually peddle this big bad government / taxes are bad have little-to-no understanding of economics or the cost of the services they provide. They are more efficient, yes. I also don't know how you expect people to afford or have the time to pay for all these services that they may or may not use.
What happens to the people who can't afford all the services I mentioned above?
Well you'd think food and clothes would be their first priority, but nobody is asking the government to nationalise these services...
These people would need to rely on charity, as they do now, but that charity would be voluntary rather than coercive.
And when there isn't enough charity these people just what exactly? They die... freeze/starve/bleed to death etc. And you can buy clothes with your state benefits. You can't buy them with nothing. Charities currently struggle to feed and clothe the poor as it is, never mind once all their benefits have been taken away and there's hundreds of thousands more out on the streets and freezing and starving and bleeding all over the place.