I think it was more a case of people looking at the works with the hammer of rationality in their hand and seeing lots of nails for the characters to knock in. For example, The Melancholy of Haruhi Suzumiya sets up a problem (Unehuv vf Tbq naq perngrq gur jbeyq 3 lrnef ntb ohg qbrfa'g ernyvfr vg, naq vs fur rire qbrf gura fur zvtug haperngr vg whfg nf rnfvyl), but I found that setup fading into the background as the series of DVDs that I watched went on. By the fourth in the series (the murder mystery on the island isolated by storms), it was completely absent.

With Fate/Stay Night, one problem is that I was looking at ripped videos on Youtube, while the original material is a "visual novel" with branching paths, so it's possible (but unlikely) that the people who put up the videos missed all the rationality-relevant bits.

I've not tried Death Note, but I suspect I'd find the same dynamic as in Haruhi Suzumiya. A hard problem is set up (how does a detective track down someone who can remotely kill anyone in the world just by knowing their name?), which makes it possible to read it as a rationality story, but unless the characters are actually being conspicuously rational beyond the usual standards of fiction, that won't be enough.

I'm also not part of the anime/manga community: I watched these works without any context beyond the mentions on LessWrong and a general awareness of what anime and manga are.

It's weird how the girls all look like cosplay characters. :)