Like many in this thread, I have been frustrated by music purchased from iTunes cluttering my Music app on my iPad and iPhone.
I want to control what music is on my iOS devices. I use playlists and genres heavily (but not shuffle, nor in a car). I rename Genres to give me greater control, and the purchased music defaults to its own genres in iOS which makes my experience even worse.
The two solutions that have worked for me are:
1) Use "Downloaded Music"
At first I was sceptical but as those defending Apple have argued, it does work. Just move it to the top of the iOS Music app Library via the Edit button. It's one click further, but all the sub-categories are there - e.g. Genres, Playlists, Artists, etc.
2) Switch off iTunes/App Store (i.e. sign your Apple ID out but stay signed into iCloud)
This removes all the purchases from the iOS device so has the same impact as 1). For instance, all my own Genres are now in tact as all the electronic purchases with their own genres have gone. I can retrieve the purchases later if I want them back. (Note: I have some purchased music in my playlists but they still appear correctly because - I think - I've downloaded them to my Mac first). This probably won't work for people who buy apps regularly, as presumably you'll need to log in/out frequently.
I'm sure there will be issues as iTunes (and Photos) seems to be increasingly poorly designed but, for the moment, it works for me.