You need to understand what the TC does.. and what it does not do.
It was always a part of the apple lineup for laptops to do backups without needing extra drive plugged in.. ie it is going to backup over wireless automatically without people having to worry about DOING something.
TC is not nor has ever been a media server. It has no part in iOS line of products. From Apple's viewpoint your ipad and iphone do not have any connection to the TC hard drive whatsoever. That doesn't mean you cannot load an app to allow you storage of files.. it is simply that Apple designed it so that iOS either links to the computer.. and will backup via iTunes on your computer or to iCloud.
Ease of access across devices is totally iCloud.. there are no server extensions in the TC to do anything.
So the one and only "official" use I can see for a TC in your network is Time Machine backups from your MBP.
Otherwise it is merely a wireless router.. and an Airport Extreme or another brand will serve you just as well.