We teach mathematics backwards and in the wrong order and we push students through things they have not mastered.
"A Mathematician’s Lament" by Paul Lockhart
BOOK published in 2009 https://www.amazon.com/Mathematicians-Lament-School-Fascinat...
We're having two different conversations here. You are saying (correct me if I'm wrong) that the algorithms you use for parsing are broadly applicable to program analysis. You are not wrong. It's just orthogonal to my point, which is that program analysis is really interesting.
To make an analogy here (from Lockhart's lament: https://www.maa.org/external_archive/devlin/LockhartsLament....), you are saying that color theory is massively important throughout one's career as a artissti. I am saying that I just like painting things.
Sure, there's lots of cool shit in parsing theory no doubt, with tons of broad application. But the way that we are taught it ("here's how we get an AST from written text") turns away people who are into program analysis. As such, we shouldn't consider parsing a pre-requisite for program analysis, regardless of how interesting or applicable the theory of parsing is.
This complaint about the way math is currently taught, and the ensuing new approach, both remind me of "A Mathematician's Lament"  by Paul Lockhart.
I think you this will interest you. Its a mathematician's lament on how the current system of teaching math is wrong.
Interestingly, there's a paper "Lockhart's Lament", on math education written about 15 years ago that proposes an absurd world from a musician's nightmare where formalized music education is mandatory but playing music is generally discouraged.
The point, poorly summarized, is that it resembles math education where a soltary focus on calculation distracts from learning how to do the type of math that only professional mathematicians seem allowed to do now.
It's worth reading if only to see how it often seems like the grass is greener for the educational environment of other fields.