The bias on anime is some of the most ridiculous there is. I mean, wow, it's pretty obvious most of the people saying these things about anime have no actually experienced it with opened minds and probably base their entire opinion on the people who like anime.
Let's get one thing straight.
You know those 300+ pounds, wizard-hat wearing freaks who live in their parents' basement and like to pretend they are Gandalf on their free time? Do they represent DnD? No, so if those "otakus" are a deciding factor on your opinion about anime, even if you don't realize it, don't let it be. The lowest tier of geeks are annoying, no matter what they are into.
For the sake of simplicity, I mean both manga and anime when I say Anime. In my own opinion, manga is much superior to anime. Some will say the same compared to comics to cartoons.
Now, this point has been said again and again: Anime(and Manga) is not a genre, but a media. Anime are Japanese cartoons first, subculture far second. It just so happens most anime is fantasy(including supernatural and science fiction). However, anime isn't limited to fantasy either. Romance/drama, comedy, and horror are all popular themes.
I'm even willing to go as far to say that anime is more varied(in the mainstream) compared to American cartoons(in the mainstream), at least in recent history. When is the last time you've seen a dramatic cartoon, without superheroes? For America, things seem to be split into the following: (Children) Humor(the old classics like Bugs Bunny, Spongebob, ect), Action(Superhero shows, Avatar[which is anime influenced], Ben 10, ect), and Adult Humor(Everything on Adult Swim, South Park, ect).
And there is one very big factor is missing in American cartoons(but not comics) which is very common in Anime: Character/Plot development. Action anime is almost always split into arcs and chapters. This is either rare or slow in American cartoons, only happening in session premiers and finales most of the time. Anime is more like manga/comics, which for storyline purposes is almost always better. This is because most anime usually started out as a Manga... Manga is very, very popular in Japan, more popular than Anime. Imagine if Comics were more popular than Cartoons.
The Marvel series cartoons X-men and Spiderman are considered some of the best cartoons. This is because they were based more on comics than most action shows. This formula seems to be less and less apparent in America, even in Superhero shows.
(1) Cult of Youth - everybody assumes that your 15-year old girl should be able to be a ninja/swordmaster/olympic gymnast, or maybe also a wizard and ranger if she's so long in the tooth as to be 17 years old (practically out to pasture!). If you haven't made Epic by the time you're 19 you're probably an NPC.
Since when was this limited to Anime? I mean just look at Elves, they are practically eternally youthful. In almost every media that comes to mind, action heroes are usually young and dashing. Anime did not create this, not by a long-shot.
(2) Soap Opera - so the teenaged girl with Death Star-level psychic powers and the teenaged ninja/swordmaster/gymnast girl are having an affair, but the teenaged ninja/swordmaster/wizard boy likes the psychic girl, and how can he compete with Ai for Noriko's favor because he's only a wizard and not a gymnast, and maybe if he buys her roses in the next town blah blah blah. None of which has anything to do with exploring the Mad Wizard's dungeon. Unless someone casts Power Word Angst.
Again, since when did this come from Anime? Are you telling me that the Japanese invented the "human condition" in the last 50 years? If I recall correctly, there was back-stabbing, love affairs, and couple problems since the dawn of civilizations.
(3) Attitude - I have the suspicion that anime is partly behind the "Dungeonpunk" style of 3E. Obviously nobody can be a hero without asymmetrical spikey bondage clothes and wacky hair. These things are almost as important as being a teenager and having pointless angst.
Wow, third one, and still not spawned from anime alone. Spiky-clothing/armor have been popular since forever, at least if half the Roman gladiator art I see is true. Wacky hair is exotic, and fantasy loves being exotic. Again, angst isn't a man-made creation, and if you are dealing with teenager-problems in your game, it's not DnD, it is your players.
There is not an argument I've seen so far that makes a lick of sense. If I say anime influence my game, do I mean Naruto? or Bleach? or Death Note? or Love Hina? or... ect ect. The fact that anime is usually grouped together by art, not dialog or plot, makes this conversation even more pointless. What are you doing? Drawing as you play?
Do I think DnD represents Anime well? No. DnD can't represent any story decently. Not even LotR or Conan. DnD is DnD, and it's also a game.
the third most disgusting thing in the world (not including illegal stuff)
Why? I'm willing to bet you can't even say why.