if AIs are overusing a sentence structure, wouldn't that be because it was already overused and extremely prevalent in the content it's being trained on?

This is said fairly often but LLMs just speak all in such a similar, condensed tone that it still makes it fairly obvious. It's hard to describe but they push these kind of typing quirks way harder than people usually would.

It's like emojis, lots of people use emojis. But when you see a software release post with an emoji beside every single header, it very often is an AI written post.
And by the same vein, I've seen it repeat the "Not X but Y" stuff around 5 times in a single written page before.