You are absolutely right.
I have often been surprised by some GPT4 brilliance after pushing it to think harder in an extended back and forth.
Seeing it recover from a misunderstanding on something complex with an epiphany, and an immediate recognition of all the implications is a joy to behold, as well as useful.
And on occasion, when I have pushed it to correct itself, and it recognizes I am misunderstanding something and checks me, what a time saver!
I particularly like how frequently it provides a concrete example, before making a general statement, when dismissing some math related argument.
Gives me the warm fuzzies to have a bright, curious, tireless, if precocious, “friend” on tap.