This money was needed for public expenditure and to keep the Greek banking system running.
The biggest creditor banks of the Greek state were, in fact, Greek (ca. 50–60 bn. Euro).
The biggest foreign creditor banks were French (ca. 42 bn. Euro).
Accordingly, France was for more financial support (for Greece) to be payed by all EU member states.
The German banks were only a distant third (ca. 25 bn. Euro). But the German state was the biggest donor among the EU member states.
That is why Germany and some other net contributors e.g. the Netherlands were not too keen on keeping Greece in the EU zone at all costs. For them, the solution you named (“defaulting and keeping the euro”) would have been the rather advantageous, but not for Greek nor for other powerful member states. Nor for the Greek oligarchs – remember, Greek is a country of only about 10 million people who were not that well off – in whose hands may have ended most of the 360 bn Euros of the old debt? They liked the toxic fairy tales Varoufakis was telling (married to a member of the Stratos family).
That was indeed the "mainstream media" (I so hate that expression but it does apply) opinion. The reality is more prosaic: German (and French, but mostly German) banks would be screwed if those debts were defaulted upon.
Look at the GDP per capita of Greece since 2010. Looks like staying in the Eurozone didn't do them much good either...
https://data.worldbank.org/indicator/NY.GDP.PCAP.CD?location...
Just fyi, Hungary had a ton of homeowners with loans in EUR and CHF and when the HUF collapsed the rates became untenable and the government just said "eh, fuck the banks, let's keep the previous exchange rate". The banks survived too.
It's a hard political decision but not an impossible one.
(Disclosure: I deeply disliked that government for other reasons and didn't have a loan, it was just interesting to see populism in action without obvious downsides materializing)
But in the end, it was clear that unlike in Iceland, bankruptcies were not considerable, and so a bailout was going to happen. The only question was how the bailout would be structured.
Yanis Varoufakis made his name back then by going against the grain and proposing a hairsplit, but instead an approach was chosen where Greece never really defaulted, but its population was harshly punished for it.
Reintroducing the Drachma was a "solution" to the political problem of cutting spending by creating hyperinflation, not anything else. So it makes no sense to default and keep using the Euro. The reason for defaulting is because you don't have enough euros....