If you know Japanese then it makes it obvious that something strange is going on in English too, but it is not important. Forget I mentioned Japanese.
Why do posture verbs refer to states and not movements?
Why does "sitting" refer to the a state of being seated, rather than to moving from the erect to seated position, why does "sitting" refer to "having sat"?
Why does "standing" refer to the erect state, rather than to moving to the erect position, why does "standing" refer to "having stood"?
"Taking" does not refer to "having taken". If I am taking a piece of cake then I am holding a piece of cake and moving my arm away from the table towards my plate.
"Throwing" does not refer to having thrown the ball. If I am throwing then then by arm is in motion.
Posture verbs are not like other verbs.
Is "standing" (refering to a motionless state) in the present continuous because the act of standing is often brief (only guardsmen stand for more than a couple of hours), because it is intentional (if one did not keep trying to remain standing one would fall down), or because it is reflexive?
Reflexivity does seem to be important, but there are many verbs such as "hitting myself" which refer to movement, not to having hit myself. The reflexivity of posture verbs is embedded. In the (slightly archaic) phrase "He sat himself down," suddenly the present continuous "he is sitting himself down" does not refer to the seated state, but to the act of placing his posterior on a seat.
This is an important point but I am not sure why embedded reflexivity should turn a verb into a state verb into a stative present continuous verb.