In programming the simplifications has to be correct even if you don't prove them, and being correct isn't that easy.

Pedantic: how do you know something is correct without proving it? How do you know you have covered all possible edge cases? /Pedantic

In all seriousness, the intersection between correctness and project delivery is where engineering sits. Solutions must be good enough, correct enough, and cheap enough to fit the use case, but ideally no more than that.