I'm not trying to create a straw man; what I'm suggesting is the futility in such a deliberate action. He's chosen to resign. What good does it serve to do so, just to influence his immediate successor? What he'd be saying is that "I don't trust my cardinals, I don't trust who they might pick were I to die or become so incapacitated that I couldn't influence them."
So my question to you was, if he could not influence future Popes, what difference would it make to influence his successor?
So if I can't influence a thousand years from now, I shouldn't try to influence tomorrow?