The central problem with a common currency is that when a country loses competitiveness, it has to solve that problem by cutting costs. I.e it has to undergo a period of deficient demand or “austerity” in order to get its costs down. That is not ideal, to put it mildly.
An alternative is for a country to have its own currency, which means that given a loss of competitiveness, it can devalue its currency. That means that, at least in theory, full employment can be maintained while competitiveness is restored.
That’s not an entirely free lunch: that is, the price of imports rises which hits living standards in the relevant country. But what’s wrong with importing less food and growing more of it yourself? What’s wrong with importing fewer foreign cars, and making more of them yourself? Not much.
A third alternative, is to implement import tariffs. That has the same effect as having your own currency and devaluing. So the advantage for Greece would be that it could revert to full employment. It would grow more of its own food: and note that Greece does import an awful lot of its food. See this article entitled “Why does Greece import so much food?”
Of course tariff reduction and abolition is one of the basic purposes of the European Union. But desperate times call for desperate measures, as the saying goes.
Allowing a country in a Greek type situation to impose import tariffs would be a sort of “last chance saloon”: a final chance to get their house in order before being forced out of the Eurozone.
And that's not to suggest that having your own currency and devaluing, or import tariffs would necessarily solve the problem. It's widely appreciated that the elasticity of supply and demand for a country's exports and imports can be such that devaluation does not work. And in that case the country is done for, or at least "semi-done for". I.e. the only solution is for a proportion of the country's citizens to quit the country and get jobs elsewhere. And in fact that's to some extent been the solution adopted by Greece for a century or so: there is large Greek diaspora in the US and elsewhere.
But the import tariffs are worth a try aren't they? Why is no one discussing import tariffs? Darned if I know.