This doesn't mean what you think it does. It's still going to be just as "socialised", except that it's going to leave more decisions up to the doctors themselves. It is trimming the fat, but don't make the mistake of assuming every "Leftist" wants as big a government as possible.
This could be a good thing or a bad thing depending on how it plays out.
The NHS is not exactly a stellar system compared to the French or Nordic systems however. It should also be pointed out that you can opt for private insurance in the UK & Ireland. My mother does, it came in handy when dealing with her recent breast cancer however from other stories she's heard those without still got a fairly good level of treatment.
Being out of work for quite some time, she is going to have difficulty paying the insurance however, which could be awkward in future as she's getting old and more prone to other health issues.
One of the virtues of the US system is that they do deal with cancer very well and has better survival rates than here as our system is horribly mismanaged. I imagine under a more conservative/libertarian system, the "personal responsibility" card would be played(which is nonsensical as anyone can get cancer, even if a healthy lifestyle helps) which would be very worrying.
It shouldn't need to be pointed out that the cheaper a doctors visit is, the more lives you can save. I have a friend who was bleeding from the anus and wouldn't see a doctor because he didn't want to pay $50+ and have it end up be something minor. It's crazy.