I love your min delta / max delta metaphor. It does explain why many of us are good at one side of the teaching / research spectrum but bad at the other.
There is another aspect to acquiring knowledge that turns this around. As teachers we want to create moments where the student recognises the true nature of a relationship, beyond the rehearsed formula. Those moments require the student to see the familiar afresh, and then to re-construct their earlier half-knowledge in new terms. This makes the teacher a delta maximiser.
Russian literary theorist Viktor Shklovsky (an outcast under Stalin) developed an entire theory of aesthetics based on this concept of "defamiliarisation". Art for Shklovsky is meant to break the false safety of the habitual view.
"Art exists that one may recover the sensation of life: to make the stone stony."
This too is the role of the academic teacher. To let the student experience the stonyness of the stone.