Maybe because the app could be a mail client? If I downloaded a mail client and it wasn't able to delete my email I'd think it was a pretty crap piece of software. The same as I'd expect if I wanted a fully featured mail client to connect via IMAP.
I'd also feel a bit annoyed if a Twitter client I was using was unable to delete tweets, and I had to go back to the Twitter website to do that.
The thing about making APIs to let other people interface with your product is that you have to expose all the functionality of that product, or there's not really any point.
There are some fair comments in this thread saying that the "manage" permission is significant enough that it should be flagged a bit (or a lot) more strongly than the common "identify" permission, but personally I don't think the point of the API is something that needs questioning.