He's arguing that, essentially, countries like Italy, Spain, Greece etc cannot reform their cultures and without the Euro would effectively be forced to re-calibrate their economies by a sinking exchange rate. That is, they'd be unable to afford foreign exports so they'd buy more domestic products, and that in turn would grow their economy. But in the euro there are no floating exchange rates, and people are very reluctant to pay themselves less, and governments are very reluctant to pay out less in benefits, and the EU/ECB is very willing to finance all of this with money printing and huge bailout "loans" .... so in the end there's no incentive to reform or make it easier to get things done.

Convenience of currency changes when migrating is certainly not the issue at hand.

Contrast with, say, Venezuela, where there's a fake exchange rate propped up by the government that the average person cannot get, and you start seeing some actual monetary friction.