It's easy to imagine why something could never work.

It's more interesting to imagine what just might work. One thing that has plagued programmers for the past decades is the difficulty of writing correct multi-threaded software. You need fine-grained locking otherwise your threads will waste time waiting for mutexes. But color-coding your program to constrain which parts of your code can touch which data and when is tedious and error-prone. If LLMs can annotate code sufficiently for a SAT solver to prove thread safety that's a huge win. And that's just one example.