Slowly, indeed, Nfk.
It's taken 60 years for 19 countries to change to the Euro, 2 countries to co-operate with defence, 22 countries to agree to Schengen (though a number of non-Eu member countries clearly think it's a good thing, too). The European Court of Justice is for settling trade disputes, other trading blocs have their own dispute resolution arrangements so we wouldn't be free of them. Or are you confusing it with the European Court of Human Rights, which is nothing to do with the EU? And wasn't the Common Market a 'Good Thing' (as lots of Leave voters have told us on here, fine with the EC but not with the EU?)
At this rate of progress I reckon that we'll not only be long gone, but also our grandchildren, by the time the idea of Europe as a country becomes a reality (if it ever does)