Scarecrow is an ENTJ. he just wants to prove he can do what he said or thought to the world. INTP's dont want to prove anything, just like the Joker, They are happy they know the information they know, but dont any problem discussing it... or in this case showing u. like joker, he didnt try to prove u wrong he just points holes in ur theory. Batman is an easy ISTJ. Joker like him because batman was close to his Ti nature (Si + Te looks like Ti). and INTP dont look like an ISTJ but that calm lightning storm goin on in his appearance speaks to jokers Ti. an Entp or E/INTJ wouldnt care , in fact would want him dead to stop him interfering.
As far as theatrics, Intp are one of the beat actors, cuz we are continously in costume. Peter Parker is an introvert, but when he's spider man he seen as an Extravert, so why cant a villian do the same. If he was really afraid of being in public or getting caught, then how does he get away with dressing as a regular in broad daylight, he's the only villian who doesnt where a mask or hide behind a wall (Literal or metaphorical). WHo says an INTP doesnt get bored and commit a react act, we dont have a plan, we have a goal and certain things that need to take place, and the rest is impromtu. Essentially an ENTP but without the natural Fe to make us seem as weird as early as an ENTP does. At First they thought joker was just a regular nut case, but with time like the INTP u find out he's a special case of crazy. Organized noise