> the LLMs were trained to mimic how people speak (write)

It's a foundational model (fresh from autoregressive pretraining) that approximates the probability distribution of human texts. And, no, it's not the statistical average of how people speak. It approximates how a person who could have written a text in its context would have written the next words.

Fine-tuning, RLHF, reinforcement learning change this probability distribution. I guess, it's mostly RLHF that shapes the way LLMs write. The similarity of style is due to common providers of RLHF data.