Unlikely. It's more work than necessary and systemic/cultural change follows the path of least resistance. Formal verification is a new thing a programmer would have to learn, so nobody will want to do it. They'll just accept the resulting problems as "the cost of AI".

Or the alternative will happen: people will stop using AI for programming. It's not actually better than hiring a person, it's just supposedly cheaper (in that you can reduce staff). That's the theory anyway. Yes there will be anecdotes from a few people about how they saved a million dollars in 2 days or something like that, the usual HN clickbait. But an actual study of the impact of using AI for programming will probably find it's only a marginal cost savings and isn't significantly faster.

And this is assuming the gravy train that programmers are using (unsustainable spending/building in unreasonable timeframes for uncertain profits) keeps going indefinitely. Best case, when it all falls apart the govt bails them out. Worst case, you won't have to worry about programming because we'll all be out of work from the AI bust recession.