I'm another one who learned how to diagram sentences in junior high (Catholic school), and while it appears to have little to no function outside of torturing students, it gave me a thorough understanding of how grammar functions. When I went to a public high school, my ninth grade honors English teacher had a notorious test in which we had to write--word-for-word--textbook definitions of each of the parts of speech. A single error, and you got an F. She ran this test every week or so for a couple months until everyone passed with 100%. The thing was, having done all that diagramming in middle school, I could easily explain what a noun, preposition, or adverb was, so it was only the rote memorization of the definitions that took me a few tries. Meanwhile, most of the other students were encountering the concept of parts of speech for the first time.
The knowledge gained from diagramming is also helpful when learning foreign languages. If you already know grammar inside and out, you won't be trying to figure out linguistic concepts at the same time you're learning how another language handles them. There's a reason there is a whole line of books on "English Grammar for Students of [other language].