I can definitely see how a more advanced student can get a ton of valuable insights about the "abstraction leaks" of opamps, and I would even submit that opamps could be a particularly fertile place of such leaks (for our more software minded brethren: opamps are like databases: they are perfect until you start to push their boundaries and then you very quickly start to see just how imperfect they are), but I doubt you can teach a student enough about the theoretical math to get a useful intuition about the behavior of opamps in under 2 weeks.

Indeed, but you have to grasp one before it makes sense to learn about the other, and neither is going to happen in a 101 class.