Why isn't anime critically analyzed like other forms of literature or entertainment?
I think the simplest answer is that anime is just not that popular. Though immensely popular and gaining momentum, the anime community just isn't that widespread. If you look at it critically MOST of the anime fans are limited to the popular and mostly Shounen series such as  Naruto, One Piece, Bleach, Dragon Ball, Pokémon, Deathnote etc.

Compare it to the consumption of various books and movies and their penetration into our society. The iconism resulting from this is what raised them to the platform where it seems that more and more of such media is critically analysed. As Hakase pointed out, if you go to an anime forum/blog, you'll see plenty of critical analysis of anime, especially the history and tropes.

Another factor is the geography. The popularity of anime and manga has grown and they are an integral part of the Japanese culture. However, other places are adapting and amalgamating the same later. This will automatically lead to the feeling that anime as a medium is more targeted towards the audience it sells for, i.e. the japanese. But as an "outsider" we're not in a place to critically analyze it. The same may be true for various literary works or other media. 

A relevant example is the Indian epics "Mahabharata" and "Ramayana". I doubt that many people know it on this community, but Indians have critically analyzed each and every line of such epics as deep as it can go. Awareness of them is just limited to the Indian subcontinent, but now the teachings are spreading. The same is true with Anime.

Some food for thought: 

Anime popularity: Blogpost: A comment that I liked


  Depends. Again sales you might make the case but in terms of iconism there's no chance. Everyone knows who Batman is. No one knows who Luffy is.


A good blogpost about how to look at Anime as a medium of entertainment