I actually can see the use-case of asking someone for a large file. Having them download Dropbox is a pain, but something that is one-time use would be ideal.
Person 1: "Hey, send me that file, use this: url" Person 2: "Oh!" drag and drop
All updated in real time (so you could potentially link a whole group of friends something and see them all drop in files for an event or some-such). Perhaps a school trip or something to that extent.
Just connect it to your Dropbox account, send a file request email to the other person, and the files show up in the sandboxed AirDropper folder in your Dropbox account.
It's like magic.