Yes, I had that issue too (years ago, when they first allowed deleting the Music app). I think it might not be a problem in newer cars, but my car radio only had iPod support, not iPhone, and it seemingly needed at least one song in the music library for the connectivity to work at all.
I actually bought this 10 minute long silent song on iTunes at the time, so my phone wouldn’t automatically play Weezer’s “Across the Sea” every time I connected my phone to the car: https://music.apple.com/us/album/a-a-a-a-a-very-good-song-si...