I mean, I agree with the first part fully, but I think what you mean is that we shouldn't have for-profit corporate run insurance.
Any socialised health care is a form of insurance---a way for us to pool the risk of large bad events, so that everyone (or a lot of people) pays a little so that a few people aren't totally destroyed by the catastrophe. The alternative to having insurance is that we let people die when rare but really bad things happen. We absolutely should have insurance, but we should all share the cost equally, or the rich should pay more, rather than a few people massively profiting from running the enterprise.
But, however we run it, we'll need to treat dental differently from medical because of what I said in my first comment