I think those short courses would be more effective if they didn't bother with ANOVA and instead taught intro probability and distributions and then jumped straight to regression. ANOVA is just a really specific way of doing a regression.
In R, and python::statsmodels you get the answer to (essentially) an ANOVA any time you run an LM or GLM; its the Z-statistic for your whole model.
I know there is more nuance to this, but teaching students that they can use regression for most of the problems they would have used seemingly arcane tests for is going to be much more useful for the students.
I agree with the sentiment although I'm not sure there is the time for all of it. At least when I took them, probability theory and distribution theory were separate semester long courses, and the former was a prerequisite for the latter.
In R, and python::statsmodels you get the answer to (essentially) an ANOVA any time you run an LM or GLM; its the Z-statistic for your whole model.
I know there is more nuance to this, but teaching students that they can use regression for most of the problems they would have used seemingly arcane tests for is going to be much more useful for the students.
Here is a lovely page demonstrating how to do this in R: https://lindeloev.github.io/tests-as-linear/