I tend to agree but it probably went even beyond radio. Playing music has long been omnipresent in all sorts of venues and, as a result, there was a clear need for simple, low friction, centralized licensing.

Pre-VHS, as you say, there just wasn't the same casual consumption of video content--and, even then, it was mostly private consumption for a long time.

You even see differences between music and live theatre licensing. Music has mandatory mechanical licenses for cover. Whereas, with live theatre, a playwrite/copyright owner can refuse to allow a performance based on their work.