This is an excellent observation and puts into words something I have barely scratched the surface of. Along with specifications, formal verification is another domain that received the "just automate it" treatment in the before times.
And because formal verification with LLMs is an active area of open research, I have some hope that the old idea of automated formal verification is starting to take shape. There is a lot to talk about here, but I'll leave a link to the 1968 NATO Software Engineering Conference [1] for those who are interested in where these thoughts originated. It goes deeply into the subject of "specification languages" and other related concepts. My understanding is that the historical split between computing science and software engineering has its roots in this 1968 conference.
[1]: http://homepages.cs.ncl.ac.uk/brian.randell/NATO/nato1968.PD...