I did this for most of last year. I had all local music in Apple Music, disabled the cloud stuff, and synced it all to my iPhone by plugging it in with a cable, as if it was an old iPod. It all still worked.
In iOS Music, tapping the artist name on a song launches the artist’s cloud Apple Music page —- even if you’ve hidden paid Apple Music.
Disabling cellular data for the Music app fixes this by showing an album view of the downloaded music from the artist. However, the cloud version is unavoidable on WiFi. It’s a small but annoying example of how Apple made the classic experience worse to push their subscription product.
Thought if I remember correctly, search was still showing it, which was a little annoying. But it depends on how much you search.
I'm currently using the service right now, so I can't really check if anything has changed since last year when I was doing it.
On MacOS I think it opens to the online home page, but I use it so infrequently I'm not sure. I pretty much only use it to buy music from iTunes.
I have over 8000 songs synced to my phone, 100% from local files on my computer.
I never activate the "library sync" BS that Apple tries to force on you, because historically it has replaced your copies with incorrect or "remastered" (AKA dynamically compressed to hell) versions from Apple servers.
I've even caught it switching "library sync" on without permission during an update.
"to find that content on the phone is difficult"
How? You tap Library, then Songs. There's all your music.
You can technically still buy albums, but you can really tell its only there because it was forgotten about.