The Pushbullet folks have pushed out an update not to the Android app, but to the Chrome extension, that expedites the whole file pushing process. Now when the need arrives to push a file to all of the devices under your account, instead of sending them off one at a time, the extension will let you target all the things. This is functionality that the Android app and the Pushbullet website already have, so consider this more of a step towards feature parity across the board.
It's becoming increasingly common for users to share files over mobile devices instead of more traditional methods. The biggest problem here is that there isn't really a "standard" form of sharing - unlike with emails, SMS messages can't handle file attachments, and MMS isn't the most practical way of sending most files (not to mention that not all phones can receive MMS messages). There are, of course, things like Dropbox and Google Drive that store files in the cloud and make them easy for users to share, but that can be a cumbersome process on a mobile device.