I guess if you're in a situation where you might be asked for an id for the discount (a shopping day?), perhaps bring it along that day. Worst case, if asked for an id to verify for a discount, and you don't have it - you might not get the discount.
We have actually been asked for ID very, very seldom, but it's not never. I respect both sides, but we're in the camp that our IDs are always with us when traveling, just in case we're asked to provide it, or if by some great misfortune we have a medical emergency......