Thinking about this further... what if you could look at the properties of an application in the Overview, which would present a list of all the file types that the application could open. Each list entry would have a checkbox indicating that the application is the currently chosen default for that file type; and there would be a button saying 'use this application for all the above file types' which would click all the check boxes.
Obviously this needs more work (the Overview has no way to indicate that an application might have such a properties window, nor does it give the user any opportunity to interact with an application except to launch it) but I think it might go some way towards satisfying your use case.
Out of interest, what DE do you use? How do you set a program to be the default handler for one or more file types under it?