I prefer to use dropbox myself. Given the fact that most of the files I'm sharing with others are changing frequently, it makes little sense to copy something to my phone and iPad directly that will probably be out of date in a few hours anyway. But if it's on dropbox, or box, or Google Drive or some other cloud service, then the updates are pushed to all of my devices, and I'm not having to juggle multiple copies on multiple devices (work Mac, home Mac, MacBook Pro, iPad, iPhone, random linux test box).
For this reason, to me it makes sense that there's no direct access to a file system, and the storage on an iOS device isn't treated like a regular drive. Most of my content creation is happening on desktops and laptops, with only very minor edits reserved for iOS devices, which are used mainly to review and consume. So, having a cloud-based system to pull these files down makes better sense.
And yes, it's a third party, but frankly, Apple is a third party, too, and yet we seem to be fine with trusting our information with them.