There were short films produced in the 1920s and '30s, like Bessie Smith's immortal take on St. Louis Blues. Those continued through the '40s and were shown in movie theaters along with the cartoons and newsreels and such. They didn't make a ton of them, but they did make some. In the 1950s, as television rolled out across the country, time blocks weren't like they are now - there were five minute blocks, fifteen minute blocks, half-hour, hour and 90 minute blocks that would contain a wide variety of content, some of it some music act in performance. At the same time, Scopitones were popular, which were jukeboxes that played short movies of performers singing the hits of the day.
In the '50s and '60s those shorts began to be incorporated into full-length movies so you'd have a band doing a few songs or a bunch of bands doing one or two each, and then some teenage hijinks stitching a storyline together - think Beach Movies or Teenage Romance type stuff, and movies that featured a band like The Beatles or Herman's Hermits or whomever. More productions, more popularity and more available tools meant that bands like The Beatles could do short films for songs and variety shows like Ed Sullivan would snap them up and show them, so there was an outlet for the bigger bands to do that.
So no, visual content of music performances and interpretations have been around as long as there has been sound connected to pictures, and Strawberry Fields Forever was not the first time it had been done. The generation of content accelerated as the availability for viewing became more widespread, and once record companies, flush with cash, had the money and the talent and the tools to make these enduring advertisements for a launching channel that would play this content, it exploded. Don't forget that MTV was not an overnight sensation - it started out taking this content, which had been shown on local New York cable and independent channels, to a regional NYC-area audience. It wasn't even a 24-hour channel in the beginning. It took some time for it to grow beyond that area and eventually spread across the country. You may have come across those "I Want My MTV" ads where rockers would say that between commercials and songs - it wasn't picked up by cable systems and it took a couple years to grow into the massive thing it became.