in practice, with iCloud Music Library turned on, you can do what you said in your first post. Drop a song onto iTunes, it will be added to your iCloud Music Library, and a small time later will just show up on your phone. The biggest issue most people seem to run into is that initial setup of iCloud Music Library, which seems to succeed/fail to wildly varying degrees.
Anyway, I see what you are saying. Rather than go through potential hassle, just keep the two libraries separate. For me, it seems overly cumbersome to say "well if I want to listen to this song I have to go into this app, but if I want to listen to this song I have to go into a different app." I only want to have to go to one place to listen to ALL of my music. And I'd guess, removing the frustration of a horrible setup, that's what most people would love.
As I've suggested with others, at the very least I would attempt (one or a few times) to get your library into iCloud. Maybe it will just work the first time, maybe it won't. But at least give it a shot. Because if you can do it with minimal hassle, it to me seems truly like the best option.