The single currency tied the economies together, it allowed Greeks to use the cheap credit of the German economy to buy what? German cars. Germany's export businesses grew hugely because of the real value of the euro was weaker than the Deutsche Mark.
This is a problem where no single party is at fault. Yes, the Greeks were irresponsible with the credit but it's not the full story.
Apart from that, I agree with your points about the general economic union. Without a peaceful political and cultural one, it was doomed to fail.
Countries that "import unemployed people" do so for their own good. Or do you know a lot of Brits currently willing to do housecleaning work or have a factory job? Switzerland is a good example of that. ~30% foreign workers, most of them doing the jobs that Swiss people themselves would rather not do. It's very easy to blame people from other countries for you own problems, but they're paying their taxes too, just like anyone else.
Plus, Germany exports a lot to other EU countries. It's not like they're in the EU for the sole noble purpose of European prosperity.
It may look fine when you sit in Eastern Europe and get all the funds. But think for German taxpayer for a while who now has to pay for your infrastruture, meet your debt obligations in case something goes wrong, and import all the unemployed form your country. How much longer do you think Germans will take it? Of course, it's nice to be on the receiving end. But being in an economic crisis + having your own unemployed + tax hikes for your highways, do you think this makes EU popular among German voters? No, it doesn't. If Germany was given a chance there is a good chance they would opt to exit as well.
Eastern Europe is very pro-EU because it is bribed by all the money stolen from the Western Europe. But nobody, really nobody, in the West wants to stay on the board of the Titanic anymore.