Delete Play Store Access Without Removing Playback Services

I've built AOSP for the kiddo phone. My goal was to remove the Play Store so that it could not install games or other applications.

However, we use Google Fi for our phone service, which requires Google Play services to work. This is not a problem with Open Gapp. However, I would like to delete the Play Store, but retain the services of Google so that the Fi application can be used.

From what I can say, the Play Store and Play services seem to be married (that is, the removal of Phonesky.apk with Titanium Backup removes both the Play Store and Play services. ).

Is it possible to remove the Play Store while maintaining access to playback services so that the phone can still register via Google Fi?

Note: this is a rooted pixel 1. AOSP is not a strict requirement, it's just something I was trying to use to solve my problem. If this can be done, that is, the ROM in stock, that would be fine too.

Note 2: I realize that the Play Store can be disabled in app settings, but this kid is smart enough to understand that. I've also tried to hide it in Nova Launcher Prime, but it still shows up in search results in the launcher.