Intelligent/interesting video, but I don't agree with the core argument:
@IPunchCholla has covered much of what I would say already.
As the narrator says, melody survives in soundtracks of movies for children and period pieces, where it fits nicely. Personally, I think melody is the least interesting/enjoyable of the four major elements of music he describes. There's nothing wrong with expressive use of melody, of course, if we don't overdo it, rely on it, or put it everywhere in everything. But now that we're past the rather long period of western musical history where melody was dominant, music is much better, more diverse and more sophisticated for it. And we have modern/avant-garde composers like Stockhausen and Reich to thank (or blame) for deprecation of melody and influences we can trace through King Crimson, Eno, the Beatles, the Residents, the Who, the Dead, Kraftwerk, Underworld, GY!BE, the Orb, DJ Spooky, Aphex, Björk et al to many current artists and genres.
I listened to the follow-up video
What Makes Good Melody and it was also intelligent, but posited on the same tastes and biases. The things he loves—lines of expressive melody pulling you through an emotional/empathetic journey—I often find melodramatic and schmaltzy. He seems entirely committed to music as narrative. Which is just one avenue for enjoying music.