These days, file transfer apps are doing much more than just transferring files. Readdle's, new intro ReaddleDocs, file transfer app, does everything it's supposed to do and then some.
iPhone and iPad apps tagged "WebDAV."
"Files" Provides Data Storage on the iPhone - Sort Of...
The iPhone comes with either 8Gb or 16Gb of memory; why shouldn't you be able to use this memory as a giant USB stick to store your personal files / videos / mp3?
The answer is of course, that you should, but that Apple wants to control as much of this as possible.