Is it smart to simply delete all of the mail that SpamAssassin flags as spam?
No. While the vast majority of flagged emails will be correctly labelled as spam, it is not possible for a computer to be 100% accurate every time. If you immediately delete all flagged email, you run the risk of losing legitimate emails that were mistaken for spam. This risk increases as the sensitivity of your filter increases. When you make your filter too strict, legitimate email is more likely to be mistaken for spam.