We can't talk about fingering without considering how wonderfully unique every hand is and how precisely it responds to the slightest impulses. Add to this how variable pianos are and how infite the touch and articulation potential of each. In the light of these two rich givens expecting that one should or might want to use the same fingerings every time one plays a passage is to reduce piano playing to the merely mechanical.
The piano is not like a stringed instrument, on which the placement of the hand in certain positions is critical to developing a sense of how the instrument works. Also, unlike stringed instruments, we don't have child-sized pianos! I work out detailed fingerings only for extremely awkward passages though when performing I let my fingers go their way. Wanda Landowska expressed it perfectly when she said that the fingers find their way just as horses find the way home in the snow.
Even young children, given the freedom to cultivate the responsiveness of their hands, enjoy the heightened sense of mastery that comes with fresh experience every time they play a piece. They don't anticipate a repetition of a prior hearing and so they develop their own standard for performance. Their standard tends to be quite high as is their delight at achieving a particularly pleasing color or articulation.
The powerful connection between the ear and the fingers is too important to be assumed -- or anesthetized.