I think you're being too gung-ho about the difficulties the Greek government would have faced in navigating an exit from the EU without a clear popular mandate to do so. Even with massive popular support it will not be easy for a government to do this, particularly a country with as many socioeconomic problems as Greece.
I'm not. Project fear is always deployed against those wanting to end some the EU political arrangement. "It'll be worst if you change things"!
Recall brexit. The sky would fall the day after the referendum if people dared vote leave. Then it would fall if the UK dared not sign the EU's "deal". Ireland would go into civil war, the Channel ports would stop, people would die for lack of medications. and pigs would fly!
But none of that happened. Things carried on, the EU no longer legislates for the UK, its "backstop" temporary deal is about to expire and all dire predictions have been proven lies.
Greece could and should have left. Its government betrayed its people, to serve the comparatively few wealthy in Greece would would see their properties and some (few!) remaining financial assets within Greece devalued. For the "common greek" this was irrelevant, the higher costs of imported stuff balanced out by lower local costs, and a necessary and inevitable redistribution of assets and new priorities for its government. The wealthy oligarchs of Greece would flee, so much the better for the greeks.
By
fearing change, refusing change, you remain stuck in this neoliberal dystopia of "consumer" debt slavery and reducing living standards anyway. Projects fear (as done in so many countries, including yours) is about defanging the only threat to the current masters of the situation, people democratically choosing to change things.
The game is played in exactly the same way in both sides of the Atlantic. Europe will break with it first because there are so many countries and so many elections, it's harder to make fear win everywhere. The EU's purpose is to make Europe "one", prevent people in any one country from starting to change things and this giving an example for others: "but you'd have to leave the EU, it will be disaster!". Basically the EU's political project has been about emulating
one aspect of the USA: the political lock-in over the population there. But leave we will, all of us, this deceit!
The ones who wanted to change the constraining political construction here, remaining within it, were all defeated. The idiot greek finance minister, Corbyn (or rather, Labour against him), etc. Only by breaking away from it can change start. And perhaps that will be the only way to change things in the US also...