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).