It's good that you were able to figure that out, because it illustrates an important point about how "Other" gets filled: basically, any app that has temporary data of any kind stores it in Other. That includes not only downloaded video and music, but downloaded issues of periodicals and newspapers; text, photos and video in the Message app; and many other things that aren't as obvious (such as aborted sync operations). The various partial solutions that people have found for clearing out Other are exactly that: partial. No single strategy will clear out everything for all users (not even restore from backup, for certain apps).
While I don't know much about the internal architecture of iOS (and I haven't done any app development since iOS 5), it's possible to make some guesses based on the programming interfaces provided to app developers and the behavior of apps. My suspicion is that the instantaneous recovery by iOS of unused space is essentially impossible, and even a garbage collection scheme of some sort may be difficult to implement without causing other problems.
iOS isn't unique in this sort of problem. But it's probably unique in the variety of different behaviors of the apps that use its resources. It may be hard for system developers to make assumptions that would facilitate the design of useful garbage collection. The solution that Apple has proposed, as I've said many times, only partly in jest, is this: buy a bigger iPad. With prevailing patterns of use, a 128GB iPad is going to "solve" (more correctly, postpone) the Other problem for the vast majority of users.
All that being the case, if you find a solution for your particular style of use, then you can of course continue to use it effectively. But it's at best a major inconvenience. As I've also said in the past, if it's a deal-breaker for you, you can switch to a device that runs a different OS that doesn't have the Other problem. Rest assured it will have different problems that you may be able to live better with. Or not.