When studying sonnets or other poems, why do we analyze the stressed and unstressed syllables?

One of my daughters is preparing to enter a competition which requires her to recite a Shakespearean sonnet and twenty-line monologue. Like any teenager, she balked at the work of studying the stresses and pauses and such of the sonnet.

She asked why such study was necessary, and I really didn’t have a very good reason to give her. The best I could come up with was that it helped us learn where to breathe and what words to pay more attention to in speaking.

So, why do we have to study the meter of verse?