> Does that mean human intelligence is cheapened when you talk out a problem to yourself?

In a sense, maybe yeah. Of course if one were to really be absolute about that statement it would be absurd, it would greatly overfit the reality.

But it is interesting to assume this statement as true. Oftentimes when we think of ideas "off the top of our heads" they are not as profound as ideas that "come to us" in the shower. The subconscious may be doing 'more' 'computation' in a sense. Lakoff said the subconscious was 98% of the brain, and that the conscious mind is the tip of the iceberg of thought.