That is essentially how Allen Downey approaches statistical education: the analytical solutions came first because we lacked the computational power. Now that we have cheap computation, we should exploit that to develop better intuition. His Bayesian book[0] is available as Jupyter notebooks.
That's pretty cool. I actually would like to see K-12 math education use more computation and data, with less of a focus on algebra (expression manipulation). This would be more reflective of how regular people, including STEM people, use math outside of school.
[0]: https://allendowney.github.io/ThinkBayes2/