Just putting in my own thoughts on the Inuyasha characters....
On Sesshoumaru: I think his situation is more complex than simply being an INTJ. I personally believe his character arc is his development from ISTJ to INTJ; he goes from living rigidly by the external value system of youkai "society" (humans as companions= weakness, hanyous are scum) to fostering his own personal value system (taking in Rin, utilizing Tenseiga). Also, Sesshomaru early in the series is very reluctant to go about things in an innovative way- he can't see the possible uses for Tenseiga, he goes after Tetsusaiga over and over and can't seem to see the more beneficial ways of cultivating power, etc. However, by the end of the manga he's more willing to be creative about developing his Meidou attack.
Kikyou- really confounds me. How would one characterize her either post-claypot or while she was really alive? She's an I for sure, very reserved and unobtainable.
Inuyasha- SP for sure, and definitely not ESFP. XSTP seems most likely, but I'm kind of intrigued by ISFP. The question really is if an ISFP could come across like Inuyasha considering the environment/background/influence of demon traits. If Inuyasha was essentially abandoned, disgraced, and forced to live alone all his life, the hardening of his personality would be a natural result. The best evidence for ISFP, I think, is that when it comes right down to it, Inuyasha uses his feelings, rather than logical processes, to make decisions. Naraku and other demons use this strategy countless times to goad him during the series. The Kikyou-Inuyasha-Kagome love triangle is so difficult to work out because Inuyasha can't pull back and assess the situation.
Analysis isn't pointless at all. It allows for your perceptions of other people's types to have some credibility or connection to reality. (Even when ascribing said types to fictional characters...)
I agree with this. Analysis and assessment is, for the most part, never pointless. Honestly, the only reason I don't give an explanation as to why I've given a character a certain type is because of laziness. It's easier if you're typing one or two characters, but when you're typing nearly all of the characters in a series, it's a lot of work. However, I think that we should all try to do it more often. I prefer knowing the reasoning behind someone's viewpoint.