It's a prediction algorithm that walks a high-dimensional manifold, in that sense all application of knowledge it just "search", so yes, you're fundamentally correct but still fundamentally wrong since you think this foundational truth is the end and beginning of what LLMs do, and thus your mental model does not adequately describe what these tools are capable of.

Which is kind of funny because my standard quip is that AI research, beginning in the 1950s/1960s, and indeed much of late 20th century computer tech especially along the Boston/SV axis, was funded by the government so that "the missile could know where it is". The DoD wanted smarter ICBMs that could autonomously identify and steer toward enemy targets, and smarter defense networks that could discern a genuine missile strike from, say, 99 red balloons going by.

You are right that LLM and alphazero are different models, but given that alphazero demonstrated having the ability to bootstrap creations, we can't easily rule out LLM also has this ability?