Sort of. In order to be in the EU, you have to subscribe to both the ECHR (European Convention on Human Rights) and be prepared to have your laws scrutinised by the European Court of Human Rights. The ECtHR has ruled that the European Convention on Human Rights (ECHR) does not grant a right to abortion, but that there are certain circumstances where the inaccessibility of abortion may violate the ECHR. This means any individual in any country could take their Government to court. That's how it works.
The EU essentially collects an annual budget from all its members and then redistributes wealth via subsidies, the European Investment Bank, the Common Agricultural Policy and the European Development Fund. All countries pay in, but developing countries sometimes get more in subsidies than they put contribute. These countries still have their own tax systems, but these are sometimes at the local level. So, in the UK for example, where I live in London, the local taxes (council tax) provides a lot of money, as a lot of people live here. In more rural areas, the council are poorer. They get grants from central government and (up until Brexit) would be eligible for funds from the EU. It's a mixed model - and it was working (but built resentment).
The issue with Denmark is that it has a falling population - as does the UK. This means that the tax burden on workers is higher. You need to find a way to redistribute the wealth from California to Florida, because fewer people are working in Florida, and they can't afford to have 1000 people working in Disneyland and 200,000 retired people eating all the public services. Would you prevent people from moving between states? The reason you've probably got a hollowed out middle in the US, is the same reason we've got 5 million people in the whole of Scotland and 9 million people here in London. People go where the jobs are - does that mean I'm paying for Scottish people? Yes it does. Does it mean I'm paying for Romanian people (it did until Brexit) does that mean all of us can create a stable world free from panicked economic migration. Sure. :o)
