Many old time Hollywood musical movies have snippets of songs that start and end just like a music video today would, sometimes even fading away to black like some 80s music videos did. Do you think in a way they were an early form of music videos before the term was even in assistance? There were also movies like Broadway Rhythm where the story line was secondary to many musical and other performances.
I've noticed that if you cut some of those scenes you basically have a music video:

https://www.youtube.com/watch?v=Sn3ZGswnBas
https://www.youtube.com/watch?v=QKcD-e05HJ8

In a way music videos have been influenced by the musicals?

Back in the late '80s/early '90s, AMC (back when it was American Movie Classics) would sometimes play a music video or two from a film featuring the popular and somewhat obscure singers of the day. You sometimes had a standalone music video as well during either an intermission of a double feature, or before the movie itself. But these were in the vast minority, and radio, live touring, and later television were the primary means of promoting themselves. 

However, most movie musicals simply transition seamlessly from dialogue to singing, just like many stage musicals still do. Though in away, the songs together are in away the first albums, and this is where the soundtrack first took off, and 1949's  South Pacific helped to popularize the LP format. Of course the '80s themself had musical movies like Fame, Footloose, and Flashdance, and some songs had independent clips, but it wasn't until around 1978 that music videos as a primary means of promoting themself started to take off, first for some early shows in the UK, as material for intermissions on fledgling cable channels like HBO and Cinemax, and of course later on, on MTV and other music video-based shows.