Most programs don't need to be rigorously perfect. If they did, LLMs wouldn't be as popular as they are right now.
If you're dealing with medical equipment or space flight, maybe there's a need. But usually the goal is to make errors _inexpensive_ to find and fix, not theoretically impossible.
First: LLMs find so many bugs and security holes in software right now. So you pretty much have to prove your stuff correct, if you don't want to get hacked into.
Second: LLMs make it much easier to apply formal methods. Just ask Claude to prove your stuff in Lean or whatever, no PhD required anymore.
That doesn't quite match my professional experience, though - there are so many companies building databases, message queues, filesystems, and similar infrastructure. Sometimes they're internal projects, and sometimes they're commercial products. I've always felt that those systems would benefit from formal methods, since they're usually trying to provide strong guarantees to the application code on top.