Apple Music does let you do that. Anything it can’t match in your iTunes library to something that exists in the Apple Music catalogue it will upload so that you can continue to access and play that music.Oh boy I hate iTunes. Gave it up years ago. I use the cloud instead for saving / restoring my phone.
And for all my music needs i use Apple Music with 9.99$ subscription. I can listen to anything I want.
Only case where I would be bothered is if I want to listen to music from my band or friends' bands, then I guess you can upload it for free to Google Play Music and stream it from there. Too bad Apple Music does not let you do that.