The reason it's done is that the check is given to the customer for the amount of the meal, not including the tip. That's when the authorization is obtained; before the tip is added. Once the check comes back to you, you add the tip, if appropriate, and that's when YOU agree to the amount of the charge (sign the slip). It's possible, although I agree it's unlikely, that the amount of the meal might be within the card limit, but once the tip is added it could exceed the limit. That is why some banks have that policy with restaurants.

That explanation certainly doesn't explain you experience, which I agree is completely wrong.