We are close to the European Parliament. Countries like, say, Finland or Latvia aren't, though. Neither are Greece. I don't really see why anyone would want their own nation to cede sovereignty to become part of a larger, wider political union. It'd have less centrality, and less accountability, I imagine. The EU already has issues regarding accountability with unelected officials, and I imagine said issues would be heightened massively in any hypothetical full-on political union.
There'd also be the possibility of smaller, less influential nations being dominated by larger ones with a lot more pull, ala the situation in Greece not too long ago. While I'm sure there'd be plenty of US-like devolution, it seems a bit bizarre for countries with minimal representation in the EU to have issues like foreign policy (which I imagine would be a central issue) to be completely decided on by an EU parliament.
I like the idea of having close ties with Europe, I voted to Remain, and think it makes sense for us to work together as much as possible...but I don't at all agree with the idea of the EU becoming a nation in itself.