Random House dictionary (RHD) has these examples for: of (used to indicate derivation, origin, or source):
I have a favour to ask of you.
Don’t expect too much of him.
And I can add one from a Korean dictionary:
I asked a question of her.
I can guess these of’s have this meaning:
the complement of ‘of’ is an agent that will satisfy the subject’s hope or demand, from which they say ‘of’ is used do indicate origin or source. Can this be possible interpretation for those of’s?