Another way to look at it is that we’re making progress, but with lots of false starts, like most progress. Hearsay and taste are what happen when people are working with imperfect information. Probably not even Knuth has perfect information about all the studies and models that might be relevant to any nontrivial project.
The author’s point seems to be not that programmers should understand the math behind their work, but that they should do work that’s more like math. It’s true this would mean fewer bugs. But there are a lot of problems that people in the real world would rather have mostly solved by a slightly buggy dynamic program with mutation and state hiding than not solved by a formally proven program.
A lot of programming is stuff like simple CRUD web apps. I’d rather do that in Python than Haskell for the moment. If the author wants to argue that Haskell could be made friendlier without giving up its advantages, that’s an essay I would welcome.