>Are not LLMs supposed to just find the most probable word that follows next like many people here have touted?
The base models are trained to do this. If a web page contains a problem, and then the word "Answer: ", it is statistically very likely that what follows on that web page is an answer. If the base model wants to be good at predicting text, at some point learning the answer to common question becomes a good strategy, so that it can complete text that contains these.
NN training tries to push models to generalize instead of memorizing the training set, so this creates an incentive for the model to learn a computation pattern that can answer many questions, instead of just memorizing. Whether they actually generalize in practice... it depends. Sometimes you still get copy-pasted input that was clearly pulled verbatim from the training set.
But that's only base models. The actual production LLMs you chat with don't predict the most probable word according to the raw statistical distribution. They output the words that RLHF has rewarded them to output, which includes acting as an assistant that answers questions instead of just predicting text. RLHF is also the reason there are so many AI SIGNS [1] like "you're absolutely right" and way more use of the word "delve" than is common in western English.