What's wrong with it? I'm a huge MCU fanboy but the music has never really been a big part of why I like the movies so much, it's pretty much just kinda...there.
There are a few problems with the video (like ignoring how films are made, specifically when music is composed for a movie) but the biggest issue lies in their comparisons. They ask people to hum music that has been part of the cultural zeitgeist for decades, and are part of lengthy series of films and other media. The Star Wars theme has been in a half-dozen films, countless TV shows and specials, and in every bit of advertising related to the series, from toys to trailers. The Bond theme has been used in over 20 movies since the 60's. Harry Potter has had 8 movies, all using the same primary theme which is inexorably linked to the character through all media. The video suggests these three are the norm, which is absurd.
Then they present the MCU as a single series, another absurdity. At the time of the video, the MCU was made up of two separate trilogies, two movies with sequels, and four stand-alone films. Furthermore, the series' within the Marvel films make it a point not to use the same themes. There are instances of some call-backs and musical quoting, but when you sit down to watch the second Thor or Iron Man or Captain America film, you are not presented with the musical themes used in their respective predecessors. There is a legitimate criticism to be made of this practice, and, really, is the reason few people can hum an MCU theme, but that's not what this video attempts to hang its hat on.
So, instead of going "Hey, there are 12 movies in the MCU, and only 8 Harry Potter films!" and asking why people can hum one over the other, they should compare the two Avengers films or one Ant-Man film or two Thor films with other popular one- and two-film outings. Ask the average person to hum a theme from Avatar, Inception, Da Vinci Code, or Night at the Museum, and they'll largely come up with nothing. Heck, even asking for themes from recent hit series like Hunger Games, Twilight, or The Dark Knight would result in very few accurate responses.
Now, once that comparison is made correctly, you can ask why the Marvel films aren't an exception to the norm, and the answer lies mostly in what I mentioned earlier about the fact that Marvel does not reuse themes. There are some very, very strong composed lines in the MCU. Cap's theme from his first film, used for his cameo in Thor 2 is a prime example. The Avengers theme is another. But as effective as they are, for various reasons they weren't reused as thei main theme in their sequels. Personally, I think this is a mistake by Marvel, and one that at least some there seemed to recognize (with Elfman brought in to specifically place the Avengers theme into Ultron) but, again, that is not what the video is claiming.
Ultimately, beyond the rather pompous "I'm going to ignore what the director is trying to do in this scene" ridiculousness, Every Frame a Painting's video suggests that music in the MCU is poorly composed, which is categorically false. They also make the absurd claim that music following the emotion of a scene is 'safe' and 'forgettable.' That alone should be cause for derision. Finally, there's their rail against temp music, suggesting that it's a relatively new practice, and with the implication that it results in bad scores. Williams used it in Star Wars, Morricone used it in Days of Heaven, it has been a common practice throughout modern cinema, and, in many cases, is a necessity.
So, yeah, there's a lot wrong with the video. Their arguments are based on a list of falsities, and with the absence of a foundation, their points really don't stand. Granted, most people won't think to question the givens, so the video comes off appearing solid.
Hmm, wrote more than I expected, and am a few beers into the night, so if any of this doesn't make sense, I might try to explain further later.