Am I reading this right? Statistical LLM outputs pushed through a formal logic model? Wouldn't that be a case of "crap in, crap out"?

Formal logic serves as a useful filter. In other words, "crap in, filtered crap out" - remember, evolution works with absolutely random, "crap" mutations, which then are "filtered" by the environment.

That's subjective. One could argue all the things we invented in the past few thousands years were crap. Life would have been much easier in the caves, albeit shorter.

You assume it’s all crap when it clearly isn’t often enough to be useful.