Um - I don't think so... (I don't think that's a fair summing up, I mean)
I don't object to private property - I can that it can be problematic, but I think humans have a pretty basic desire to label things as theirs, and there's no point setting up a political system that works against that.
When I say private sector, I mean profit-making enterprises, specifically those that get involved in things that are necessary to health, happiness and society's wellbeing - education, healthcare, childcare, sanitary provision, transport. I'd rather pay higher taxes and have these things provided by the state - and yes, I do think the state is better at delivering these things on a universal basis (as they should be delivered). Profit-making enterprises only want to deliver these things where they will make a profit.