I don't understand the point they are trying to make.

It's very often (always?) the case that something general also solves particular problems.

    A sorting algorithm is an implementation of min()

    A parser also is a syntax checker.

    A route planner is a reachability checker. 

    A computer algebra system is a basic arithmetic calculator.

    A general constraint solver is a Soduku hint maker.

It's true that LLM output can be used as an input to another classifier, this is also true of any classifier. The improvement on top of the straight LLM classification is relatively small, and I would argue that working on the prompt or just including in the prompt for the LLM what features might be useful to consider would likely work even better.

Fundamentally I read this article as: We want to build a simpler, dumbed down clone of Mathematica, so we cobbled together the following pieces... We also needed a way to do arithmetic, so we also include a copy of Mathematica to do basic arithmetic.