The point of the bailout was to throw all the might of the State behind the sector, in a "ye shall not pass" stance that basically stated that either we cut these banks some slack or our current civilization would burn in flames.
It worked, because people got the message and business eventually went back to normal. We can disagree on whether it was "good enough" (I thought the opportunity for deeper changes was ripe, but I'm just an old-school eurosocialist myself), but I don't think any other entity could have done it except Nation-States.