What a good question!
I cannot relate to other forms of sentence diagramming; but with Reed-Kellogg, you get to know a sentence very well if you can diagram it successfully.
That is not to say that you do not understand the sentence without diagramming it, but rather to say that you take the time to really make sure you realize what is being said.
This is one of the reasons that I choose to diagram sentences from Shakespeare. These are sentences that I love. I enjoy the time that I spend with them.
If someone doesn't really realize what Juliet is meaning when she speaks the words: "O Romeo, Romeo, wherefore art thou Romeo?", I think it is a shame. That someone's life is a little less for that confusion of a noun of direct address with a noun used as a predicate nominative.
I'm glad you asked.