Well, Kirk gave Khan an option. Either a penal colony or wild uninhabited world. Khan chose the uninhabited world.
Would it even be Kirk's personal responsibility to check on Khan? Everything was logged and would be passed off to Starfleet Command. It seems like it would be their responsibility, if anyone's, to check in on him.
Not according to Khan. According to Khan, Kirk owed him a visit because HE left him there. And BECAUSE he didn't follow up, people (including Khan's wife) died. According to Khan, Kirk had blood on his hands.