I am a high school English teacher and I have enjoyed diagraming sentences
for many reasons:  My students seem to enjoy it as a puzzle. In order to
understand where a word goes, one must first understand what it does in a
sentence.  The logic of the processes permits it to become in a sense
mathematical, since more issues may be added to previous diagrams. The
question ultimately seems to be: why teach grammar at all?  Grammar is
usually taught for the sake of establishing rules and regulations of proper
writing--diagrams explain these rules and help students understand how
sentences generate meaning.  One might then ask very subtle grammatical
questions when reading poetry:  Why, for example, does Shakespeare use the
singular form of the verb in the "Tomorrow, and Tomorrow and Tomorrow..."
speech?  Why are there three ostensible subjects followed by a singular verb
"creeps"?  How does understanding this question help us understand what
Shakespeare is saying--how, in other words, does grammatical knowledge help
us understand the philosophical implications of his usage?  Similarly, in the
sonnet "When, in disgrage with Fortune and men's eyes...." why is there a
comma after "when"?    I have seen this sonnet published without the comma,
which is of course all wrong and changes the meaning? The question one might
ask a class which has been thoroughly versed in grammatical issues is: What
meanings are changed by eliminating the comma?
     The issue ultimately for me has not been diagraming in itself, but
rather the treasures of philosophical issues that are unearthed in
understanding how words for sentences to generate meaning. RonT