I guess I am mostly alone in thinking that for a system to be socialised, it has to apply to everyone or almost everyone in a country equally. From the comments and the voting, I understand that having it apply to "almost" half the population is already socialised to this time slot :)

So by your definition much of Europe (which has a robust private healthcare system) isn’t socialized?

Europe isn't a country and doesn't have uniform policies in this way. It also doesn't have things as an entity (except for a selection of laws that it's members implement differently in most cases).

Because of those facts, I have trouble even formulating a response to your question - it doesn't make sense to me.

Much of Europe has a mix of public and private healthcare, hence by your argument, none of those countries have socialized medicine.