I totally buy the correlation, but couldn’t this be a lagging indicator? By that I mean, it’s not just throwing lots of words at students, it’s teaching students lots of words and then using them. I’m not convinced “use more academic words” is great advice on its own.
The proportion of academic words used by teachers during the school day is a significant predictor of student vocabulary growth and reading achievement. Research indicates that higher teacher usage of sophisticated, academic language directly correlates to higher student vocabulary scores at the end of the year, particularly for language-minority students.