In the same way maybe what most people are "actually practicing" when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they're working on and imitating the structure of the example problem solution in order to do their homework.

Consider that you're given a magic formula (the derivative) to determine the vertex of a quadratic equation when learning how to graph equations. That nonsense is how mathematics is -taught-. It shouldn't surprise us when students adopt the "magic pattern" approach to problem-solving. (And my own experience is that most of the teachers are following magic patterns they don't understand themselves, anyways.)