I think anyone who's translated, or even studied a language with different word order than their native language, will have an intuitive grasp of the benefit of self-attention as opposed to sequentially interpreting a text word by word.

A simple illustration in German and English: "Ich liebe dich nicht," word for word, becomes "I love you not."

The nicht at the end inverts the entire sentence; if you were going along word by word, you'd have to drastically revise your understanding once you hit it.

Self-attention understands that meaning is inherently contextual, and interprets every word in a sequence at the same time. Instead of being constructed one word at a time, the meaning of the entire sentence coalesces at once.

The cool and kinda alien thing is that humans, regardless of the language they're thinking and communicating in, never do this. We're always getting the meaning piecemeal as we move through the sentence. The closest thing to an exception might be the magic interpreters do when they somehow translate what was just said while still attending to what continues to be said, holding both together and staying coherent.

The framing of LLMs as mere 'next-token predictors' misses the strangeness of how they actually process language: not sequentially but simultaneously via self-attention, which is a form of 'thinking' we simply can't intuit.