A similar example of this human over-regularization can be found speech technology, linguists have generalized 50~60 phonemes in English speech, though in real life speech, there are magnitudes more phonemes in play, if we force our speech recognition systems to classify speech into 60 phonemes, we miss out on important details. This is why end to end systems such as WaveNet is so much better than older systems, because when we ditch our over-regularized concept, it can learn more freely.
Human level _logical_ reasoning has not existed for long time and can't be the cause of human level intelligence because it is very little used in practice. Natural logic has existed little over 2000 years among subset of intellectuals as a method for reasoning.
Natural reasoning is one of the causes of human level intelligence It's basically just a bag of heuristic rules used in qualitative, action-change and taxonomical reasoning. There is no evidence that deduction has significant role in commonsense reasoning.
As a matter of fact the first logical system heavily used induction, not the duction, to extend regularity over unknown topics instead of exploring the unknowns systematically and deriving the regularities out of the experiments.
You should take a look at Pyro, and maybe try out implementing some form of variational guide for an adaptor-grammar model of programs. There are papers already claiming to have done it, just not for program induction.
I have a few ideas and intuitions to add to yours, so email me via my profile if you want to collaborate.