This channel did a pretty sloppy Hegalian dialectical analysis of Legend of Korra, which IMO revealed themselves as being talking out of their ass most of the time. Unfortunately, I don't really have any better recommendations. I don't follow a lot of media analysis YouTubers, because frankly, I think a lot of media analysis falls into the trap of essentially just confirming what they already think the messaging of the show is.
This, ironically, reveals the issue that most media criticism has in presuming that the messaging of a show is something objective, despite every other aspect of consuming art being subjective. Everybody perceives the world around them differently and comes to different conclusions despite being shown the exact same material conditions around them. Entertainment is no different. A fascist will look at most stories and find a fascist interpretation of them regardless of what the actual intended messaging of the show is, so this particular video's claim of "subtextual messaging" actually meaning anything significant just shows a completely dogmatic approach to media analysis in general.
I can't fault you too much for the whole "only watched the first few episodes before coming to my conclusions about a show" thing, because god knows you're not the first or last person to do that. I just hope that c/anime and just leftists, in general, can get over this ridiculous plague of bad media criticism.
I don't think the structure of media analysis needs to change necessarily, but I do think there needs to be a rethinking of its purpose. Most media analysis, for the most part, is fine as long as it recognizes itself as a subjective interpretation of the source material rather than an objective analysis of the messages and themes present. These kinds of analyses are fun, especially when discussing them with other people, as long as you don't take them seriously. While we're on the topic, I guess one piece of media analysis I did enjoy was ComradeRat's essay on why Kill La Kill is a Dengist anime. Of course, it's absurd to say that it was ever the author's intent, or that it's the messaging that anybody else is ever gonna interpret from the show, but it's fun to analyze the themes from the perspective.
Of course, there are examples of media where the intended messaging is very obviously stated, and there is something to be said for criticizing media with very obvious bad takes (i.e. The West Wing), but if you're at the point where the intended messaging is that obvious it shouldn't be necessary to do any in-depth analysis to prove your point. Essentially, if you need to explain the messaging to others, you've essentially just admitted that it's a subjective interpretation.