Hey,
I've been having the same issue. In fact I'm on a chat with support trying to explain it to them.
I have a solution. Since the music is not saved locally on the phone, you can delete it off your phone. You can always re-download it later for free, since you bought it, from the itunes store. Let Me explain.
I ran a test. I deleted all the downloaded music off my phone to just expose the icloud downloads. There are no songs physically on my phone right now. I started to delete one icloud song off my phone and noticed it was still playable in my library on my computer. The 'downloaded music' tab will disappear when you clear everything. You can re-sync all your downloaded content later. Be sure to have apple music toggled off in settings. It would help to have 'use cellular data' also toggled off.
Here's what you do, you take a song that has the icloud tab next to it. Hold it down and press 'delete from library'. It will disappear. Try it first with just one song notice your computer's library is fine. I know it's time consuming that you manually do each one (its faster by deleting albums), but it won't clutter your library. (I would do this method in the past to not show the parental ratings on my phone as I could hide the 'E' on itunes, and re-download from my computer).
Let me know how it turns out.
This is coming from someone at Apple Genius, "when you delete something from your iPhone it works separately from the iTunes on the computer so you will have no worries about that music being affected."