...there are games which use the analogue stick and the D-pad? They shouldn't do that --- you're supposed to hold it either by the two outside wings, with d-pad and buttons; or by the middle and the right-hand wing, with analogue stick and buttons. Using the analogue stick and the d-pad makes no sense, for exactly the reasons you say.
Okay, let me rephrase: the N64 controller has designed for people with at most two hands. Use the d-pad with the left hand and the analogue stick and trigger with the right hand is fine. Requiring the use of the buttons as well is not.