The difficulty of teaching statistics is that the maths you need to prove things are right and gain an intuitive understanding of the methods are far more advanced than what is presented in a basic stats course. Gosset came up with the t-test and proved to the world it made sense, yet we teach students to apply it in a black box way without a fundamental understanding of why it's right. That's not great pedagogy.
IMO, this is where Bayesian Statistics is far superior. There's a Curry-Howard isomorphism to logic which runs extremely deep, and it's possible to introduce using conjugate distributions with nice closed form analytical solutions. Anything more complex, well, that's what computers are for, and there are great ways (STAN) to run complex distributions that are far more intricate than frequentist methods.
IMO, this is where Bayesian Statistics is far superior. There's a Curry-Howard isomorphism to logic which runs extremely deep, and it's possible to introduce using conjugate distributions with nice closed form analytical solutions. Anything more complex, well, that's what computers are for, and there are great ways (STAN) to run complex distributions that are far more intricate than frequentist methods.