Agreed that watching others DM can improve your craft - though that's an argument for watching lots of different streaming games, rather than watching one for 100+ episodes.Not sure this explains why watching other D&D groups is popular, but it may directly answer the question of why, as a DM, you SHOULD watch.
Great Authors voraciously read other authors
Great Filmmakers watch hundreds or thousands of films
Great Musicians listen to a variety of styles and composers
Great Painters study other's art
Great Video Game designers play other games
Before streaming and podcasts, the ability to expose yourself, as a DM, to a wide variety of other DMs work was difficult, if not impossible. With streaming, you can easily do it. And the games you watch whose playstyle you don't like personally can be just as important to improving your game as the ones whose style you do like. To a lesser extent, it can also help players become better as well, by watching how other's play the game and incorporating ideas that appeal to you that you'd never thought of.
But I've been surprised to learn that most of the top boardgame designers, like Reiner Knizia and Martin Wallace, rarely play other people's designs. And many fantasy and sci-fi authors rarely read genre fiction anymore. Though in both cases they played/read lots when they were younger.