I love the "criti-hype". AI peddlers absolutely love any concerns that imply that the AI is really good at something.
Safety concern that LLMs would go Skynet? Say no more, I hear you and I'll bring it up in the congress!
Safety concern that terrorists might use it to make bombs? Say no more! I agree that the AI is so great for making bombs! We'll restrict it to keep people safe!
Sexual roleplay? Yeah, good point, I love it. Our technology is better than sex itself! We'll restrict it to keep mankind from falling into the sin of robosexuality and going extinct! I mean, of course, you can't restrict something like that, but we'll try, at least until we release a hornybot.
But any concern about language modeling being fundamentally not the right tool for some job (Do you want to cite a paper or do you want to sample from the underlying probability distribution?), hey hey hows about we talk about the skynet thing instead?
Also, my thought on this is that since an LLM has no internal state with which to represent the state of the problem, it can't ever actually solve any variation of the river crossing. Not even those that it "solves" correctly.
If it outputs the correct sequence, inside your head the model of the problem will be in the solved state, but on the LLM's side there's just a sequence of steps that it wrote down, with those steps directly inhibiting production of another "Trip" token, until that crosses a threshold. There isn't an inventory or even a count of items, there's an unrelated number that weights for or against "Trip".
If we are to anthropomorphize it (which we shouldn't, but anyway), it's bullshitting up an answer and it gradually gets a feeling that it has bullshitted enough, which can happen at the right moment, or not.