The problem is then you have the card number sitting in some online card wallet, set for Autopay or something, and suddenly it's just... allowed to charge you next month even though the card's got nothing.

Hell no, that shit should have bounced. Now you're in the hole $80 because your phone payment took an autopay from your Visa number.

Blindly allowing recurring auths to bypass the overdraft rules is utterly insane. Whoops, let's just autobill a few extra zeros!