But why?!?!?!
Because the whole architecture iOS is based on.
Simply put, there is no concept of filesystem on iOS, from an end user point of view. So if you could transfer from a given non-apple device to the iOS device, where would the files end up?
All you have is apps and each app is on it's little sandbox (means, it can only technically use it's own documents folder) and the only means to communicate between apps is through invoke commands (such as URI calls, popular for the "open in" functionality in safari, to name an example) or the clipboard, popular between music apps.
That was from an "into" perspective.
Now, the "out to" perspective. Well, since again, there is no concept of filesystem, app developers have to enable bluetooth sharing on their apps. As far as I know/remember, none of the built in apps (Apple's) have bluetooth functionality, so maybe your gripe starts when you cannot share "music" or "photos" from the basic apps on the system, but you can actually share a lot of things with different apps, like others before me mentioned.
Now my thoughts... I believe bluetooth is great and all specially for 3rd party communication of accessories (headsets, controllers, so on), but not so much anymore for sharing of files.
I understand the old "Oh please send me that MP3 via bluetooth", but nowadays, even in my country (slow 3G), I find it easier/faster to just iMessage/Line/Whatsapp/Viber somebody with say an image or a video (even if some quality is lost) that trying to send it via bluetooth.
Of course not all of this applies to all files like in "other" systems like Android, where you can send every file in your filesystem (PDF, TXT, DOC, DAT, ABC, DFG, DGDGDDHSFHFHT), but just saying.
PD: Of forgot to say, you can spread open iOS legs via Jailbreaking and then use iFile (guessing, as I don't really use bluetooth like I said before) or something like that to send any kind of file, but of course, this question was more of a "
In the non-jailbroken kingdom of Appledoom...".