You cannot have economic union without its corresponding political union.
True, but you can easily have a currency union without political union. For example, many countries use the US dollar or peg to the US dollar.
Greece could stay in the Eurozone, but the Greek government could default on its debt repayments. Of course, no-one would lend any more money to the Greek government. The government would immediately have to start spending within its means, and is that a bad thing?
The debt of the Greek government is so bad that if they default, it would completely colapse, all services suddenly cutoff probably leading to dangerous anarchy if not outright revolution. So yes, now it would be a bad thing. The EU should not have allowed Greece to be so heavily indebted but they could not force them, because it is a political issue. The greek government "decided" on that.
But this crisis isn't about that. This crisis is about finding ways to keep Europe chugging along without exposing the folly of exponentially-increasing government debt.
Also true. Even the U.S. is at risk of this "contagion".