They do allow this if the app in question has implemented iCloud drive (which all haven't of course). But you can only use iCloud drive, not Dropbox, one drive, Google drive, or local storage.
Outlook is pretty darn good for sending files from multiple cloud services via email, but again not local storage, gotta jailbreak for that. You may be able to send files from local storage via a program like documents by readle and send it through a mail app next, but that is clunky and not fun
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I feel exactly the same when people moan about me wanting an notification light on Apple devices