I think this is an interesting idea, but wouldn't it come off a bit preachy? Like "I haven't even worked for your company one day and I already know a better strategic direction to take it. Your management is useless. Hire me."
Maybe I don't have a good enough imagination on what to analyze, though.
Since I am in marketing and web development, I go through all of their online assets and their front-end code/design.
So far, this technique has gotten me 3 good paying jobs, because I'm not trying to please them in the interview, I'm trying to show them how I can help them become a more successful company. Plus you win the high ground. You just have to do it in a constructive and respectful way.
Maybe I don't have a good enough imagination on what to analyze, though.