yeah, doing real empirical stuff is messy. but that's exactly why people should learn on real data, and not in a sandbox.
There's a lot of structural econometric papers that do exactly what you ask, but you need graduate level statistics and a deep understanding of discrete choice, identification and simulation methods.
Structural econometrics is a field where PhD students, in their 5 year of study, usually produce only one complete study, if that.
I agree with the sentiment that if work is messy, teaching should have messy as well. But not when you're starting out with new tools.