I notice this reading about Voltaire and how often he is referred to as a "learned" person.
Instead it seems like we just so accept the brain is literally a type of computer that we just haven't figured out the architecture for yet. The storage part is completely trivial like a hard drive so the idea of a "learned" person is equally trivial.
But there is this strange belief that if someone is extremely skilled in a field, his genius can be applied with little efforts and training elsewhere.
You can be a Chess champion and an excellent Chef, but you this is completely unrelated, except maybe for the discipline.
Same with Philosophy and Theoretical Physics, or almost anything.
You can even be a World class Quake player and be mediocre or barely average at CS.
It is a large aggregate of abilities and skills, with some connections between them.
And we also tend to confuse language and rhetorical ability with general intelligence, because this is an ability we all have and need, that is also acting as a proxy intelligence benchmark but I don't think this ability is general enough to be used in this way.
So the fallacy behind the fake polymath is not the idea that being smart makes you better at analyzing information. It's the idea that being smart is a substitute for information and expertise. This mistaken assumption can lead smart engineers to beliefs that subject matter experts consider religious or delusional. Mars colonization is a great example in Elon Musk's case.
Btw most of the general training you mentioned isn't part of STEM and is historically associated with humanities subjects like law and philosophy instead. In STEM you typically work with set epistemic frameworks with unambiguous correct and incorrect answers. In this sense, engineers actually learn the opposite of critical thinking and discourse.