I don't know why just a default would be such a big deal, really. I can't remember ever really hearing any particularly convincing argument why a default must cause a grexit.
The reason for the original bailouts was to save the banking system. National governments took on their own banks' bad debt and the export countries lent money to the import ones. All bad debt, public and private, essentially ended up as inter-governmental debt. Whether the rest of the economy could somehow have been insulated from a banking crash at a lower cost than needed to bail out the banks is unclear. The way the banks were bailed out is, shall we say, less than uncontroversial.
The reason for the original bailouts was to save the banking system. National governments took on their own banks' bad debt and the export countries lent money to the import ones. All bad debt, public and private, essentially ended up as inter-governmental debt. Whether the rest of the economy could somehow have been insulated from a banking crash at a lower cost than needed to bail out the banks is unclear. The way the banks were bailed out is, shall we say, less than uncontroversial.