But I still don't see what the rest of the eurozone is getting out of it.
The Greek bailout, that is. I view it as a bit like the U.S. in Afghanistan. Whether it will yield anything useful from here on in can be debated for a long time. But if we pull out precipitously, and the Taliban take over, it will be seen as a big U.S. loss (whether that's worth the cost is not the question of concern here, only that it is a gross cost, whether or not it is a net cost, all things considered). Since Afghanistan once attacked us (sort of), our entire deterrent would be much less credible.
Going back to Europe, without the bailout no German or French commitment to another European nation, or another European collective project, would be worth very much for a very long time. Boo hoo you may say, but in the European world that is perceived as a very high cost indeed. It would mean writing off the major narrative of European collective progress since the end of World War II.
A second factor is that the choice is either bail out Greece or bail out some German banks. The smaller European nations are more likely to pitch in to pay for part of the former than for part of the latter. Given the size of German banks relative to German gdp, it's not even clear how much the latter is an option. The Germans have to try to keep their fingers in the proverbial dike or else all hell breaks loose. They just can't afford a run on their shadow banking system.
I view the entire bailout announcement, and its scope, as a signaling issue. The Germans loathe such semi-inflationary commitments and basically they just signaled that their banks are a good deal more precarious than the rest of us would like to believe.
So there you have it. Europe is stuck and in response to a crisis they basically raised the stakes. Arguably they had no choice, but they haven't actually eliminated the potential negative outcomes from the gamble.