A lot of people don't have internal monologues. But chain of thought is about expanding capacity by externalising what you're understood so far so you can work on ideas that exceeds what you're capable of getting in one go.

That people seem to think it reflects internal state is a problem, because we have no reason to think that even with internal monologue that the internal monologue accurately reflects our internal thought processes fuly.

There are some famous experiments with patients whose brainstem have been severed. Because the brain halves control different parts of the body, you can use this to "trick" on half of the brain into thinking that "the brain" has made a decision about something, such as choosing an object - while the researchers change the object. The "tricked" half of the brain will happily explain why "it" chose the object in question, expanding on thought processes that never happened.

In other words, our own verbalisation of our thought processes is woefully unreliable. It represents an idea of our thought processes that may or may not have any relation to the real ones at all, but that we have no basis for assuming is correct.