I think "no" has the implication of no existence of something such as "There is no person in the room", that's "why I am no taller than John" means "I have no fact or there's no fact that I am taller than John, so I stay at John's level" while "not" means the opposite of something.
Now I can understand why "He is no more than a beggar" means "He is only a beggar" as it means "He stays a beggar without having a higher state than that". "No" can be interpreted as "there isn't" instead of negation. I hope I understood it right, and I think so.
Thanks for your great teaching!