Greece is broken, and can’t be fixed

Well, that's one way to see it. Another is that Germany is exchanging the "careless loans" which written assurances and claims on Greek public property and priority payments on any future state earning well in the century. So, in essence, they are buying the whole country for cheep. (I'm a Greek. I'm also for letting Greece and the German banks default).

Germany especially has a bad history with giving loans. The German (Bavarian) appointed government when the Greek nation state was established took several loans with terrible terms, like, the lender keeping 70% of the loan amount as insurance and only giving the rest, while expecting the full repayment with interest for 100% of the amount. On top of that, those state loans were stolen by members of the bavarian government.

So, not only the Germans had their government appointed to rule the new Greek state, but they took huge loans in the state's name, of which the state only ever got less than 10%. That happened around 1830-40.

In another famous case, during World War 2, the German occupation forces forced Greece to give a loan to Germany, that they never repaid. Here's the story from Wikipedia:

Greece suffered greatly during the occupation. The country's economy had already been devastated from the 6-month long war, and to it was added the relentless economic exploitation by the Nazis. Raw materials and foodstuffs were requisitioned, and the collaborationist government was forced to pay the cost of the occupation, giving rise to inflation. This was further exacerbated by a "war loan" which Greece was forced to grant to the German Reich. This "loan" was never paid back and severely devalued the Drachma. Requisitions, together with the Allied blockade of Greece, the ruined state of the country's infrastructure and the emergence of a powerful and well-connected black market, resulted in the Great Famine during the winter of 1941-42, when an estimated 300,000 people perished in greater Athens.

Instead of repaying their WWII debt, and helping rebuild Greece that their war, occupation and forced loaning devastated, it was Greeks that were forced by poverty to immigrate in great masses to Germany after the war, to work as "guest workers", i.e minimum wage factory workers.

It was on these "guest workers" (Greeks, Turks, etc, plus money from the US that wanted to keep West Germany happy as an ally against the USSR/East Germany) that the "German recovery miracle" was build.

That said, the initial German loans in the EU era were not that "careless" in the first place: not only have the base loan amounts have been repaid (the huge debt is mostly about compound interest upon interest) but the loans were also used, along with political pressure, to ensure Greece buys mostly German products, from food and cars to construction services and weapons, and structures it's economy accordingly (EU directives, mostly devised by Germany, ensured that with laws that regulated more or less the de-industrialization of Greece and the slowdown of the Greek agricultural production).

So, the German's got their money back twice (the loan payments, plus the money from the loans used for buy stuff from them), and they still have the interests and debt to ensure that they also get assurances for the repayment of the rest of the loans/interest. Of course, they don't expect Greece will ever find a way to repay those huge amounts, they mostly want to buy assurances in the form of claims to Greek public property and political pressure to have their way in the country.