I don't think that mathematicians are actually in the best position to judge how math/logic might help in practical applications, because they are usually not interested in practical applications at all (at least for the last 70 years or so). Especially, they are also not interested in logic at all.
But logic is very relevant to "being logical/reasonable", and seeing how mathematicians apply logic in their proofs is very relevant, and a starting point for more complex applications. I see mathematics as the simplest kind of application of logic you can have if you use only your brain for thinking, and not also a computer.
"Being logical/reasonable" also contains a big chunk of intuition/experience, and that is where machine learning will make a big difference.
But logic is very relevant to "being logical/reasonable", and seeing how mathematicians apply logic in their proofs is very relevant, and a starting point for more complex applications. I see mathematics as the simplest kind of application of logic you can have if you use only your brain for thinking, and not also a computer.
"Being logical/reasonable" also contains a big chunk of intuition/experience, and that is where machine learning will make a big difference.