Another added benefit that you may not think about is your bow arm. If you do everything else right handed, your right side is usually noticeably stronger. Therefore, your bow arm should be much more solid and steady when shooting lefty. However, the sight picture is what makes the switch all worth it to me. The only time that I miss left or right now is when I get a bad release, and even then it's only off by a few inches. It's just nice to have your brain and your eyes working together for a change :D
Take care,
Jason