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Why is Gyrification Advantageous?

Standard ‘Explanation’:
I’ve seen countless neuroscience articles and experts explain that ‘cortical gyrification is advantageous because it increases surface area which obviously increases your intelligence’ (e.g. this wikipedia article).

Question(s):
But this explanation is woefully lacking, why does surface area matter at all? That implies that somehow empty space is contributing to cognition (since the alternative is that space being filled with brain matter). I don’t see how empty space can ‘think’…

My best guess:
The only guesses I have are that perhaps it functions like skip layer connections in Residual ANNs. This section of the wiki page, says it is advantageous because ‘it allows neurons to be closer together’ which I guess kind of corroborates my idea?

Question(s):
But it is still far too vague and speculative. Why could these same wiring patterns not just emerge within a smooth-surfaced brain without wasting space? Also does this imply that if you got more brain matter to fill in these spaces later your intelligence would decrease?

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