I believe that, especially absent a rather strong political and societal convergence, the other three need to allow for quite significant restrictions (for example, if a tax is introduced on carbon in one country, it must be possible to tax imported goods based on their production emissions).

As I argued in the other thread, it is the political dimension of the EU, allowing Union-wide standards to be legislated by means of directives which become binding for the member states, that makes freedoms of movement desirable in the EU.

But in the case of monetary policy, the monetary union and free movement of capital make fiscal union (with fiscal transfers) a necessity.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman