Greece: That country has massive structural problems: Corruption, a bloated administration, the rich not paying taxes... Europe isn't the cause of all the pain experienced by the Greek. It might have been handled better, but I wouldn't say it's been handled badly - had the EU not gotten involved, it would likely have gotten worse - and the crisis spread to other countries.
You are missing the largest problem of all, Greece is in a monetary union without a fiscal union.
During the good times, the monetary union encouraged a boom in Greece. They shared a currency with Germany but their wages were much lower so their wages rose. This was good for Greece, economic growth, and good for Germany, yay exports. Then the crash came and greece prices needed to adjust to it. The problem was that adjustments happen through changes in currency prices vs. your trading partners (and the expectations of those changes). But Greece couldn't adjust with it's neighbors because of the currency union. Now there are two ways out of this and neither was considered, let alone tried.
The first is the American way. The US is a monetary union but also a fiscal union. If the economy of Michigan collapses it's economy will get worse then the US as a whole but not that much worse because there's a lot of shared fiscal responsibility with the Federal government that protects the state. And because smart investors knows about this stuff they dont devalue the bonds of a distressed state too soon and there isn't a death spiral of debt interest rates exploding. But while the residents of New York are okay for subsidizing Alabama for decades on end the Germans have stopped anything that would remotely resemble a real solution, allowing the problem to just grow worse.
The second way is the kludge way. If you can't adjust your prices against your neighbors then you need to use inflation to do that instead. Labor prices go downward more slowly then upward in nominal terms but if the value of a Euro falls and the wages stay in place, you solve the problem. Now Greece doesn't control it's currency but the eurozone as a whole has a depressed economy so should want the European Central Bank to be supporting easy credit. At the very least they should be hitting their inflation target of 2%, ideally they should be exceeding it because these aren't normal times.
Instead we have this:
Inflation has been substantially below the 2% target over the course of the crisis. Massive, massive economic mismanagement. This is the economic equivalent of a doctor in 2014 trying to treat a cold with blood letting. And still being allowed to practice medicine. And winning an award for it.
And it's because of this:
Even though this monetary policy is massively destructive for the union as a whole, it's good for Germany. I don't mean to say it's all Germany's fault-.... oh wait yes I do. It's all Germany's fault.
Germany is blaming the lazy greeks but it's actually the Germans who are being lazy slobs here. During the good years, the currency union benefited Germany, the export boom and capital investment boom raised the German standard of living and was good for German prices. The the bad times came and it was time for Germany to pay up. They had gotten the benefits now they, as the big rich economy needed to do the big rich economies job. And they shirked their responsibility, insisting that Greeks work to pay off an obligation that from a rational economic sense Germans should. Then on top of that they made it impossible for Greeks to actually do that by insisting that monetary policy serve Germany, not European interests.