This is actually a great point, even when it comes to paying non-credit card related bills. When you authorize a business to remove cash from your bank account using ACH, it's a "withdrawal first, ask questions later" arrangement.
I remember seeing a news story about a gas company who had thought a customer damaged their gas meter. They replaced it, then deducted the $1000+ cost of replacement from the customers bank account. Since the customer authorized the ACH access, they were out of luck in getting the money back right away. If they hadn't linked their bank account, they would have gotten a bill and could have figure out an arrangement before handing over any cash!
I remember seeing a news story about a gas company who had thought a customer damaged their gas meter. They replaced it, then deducted the $1000+ cost of replacement from the customers bank account. Since the customer authorized the ACH access, they were out of luck in getting the money back right away. If they hadn't linked their bank account, they would have gotten a bill and could have figure out an arrangement before handing over any cash!