Interesting situation,
Before I complained beyond the individual company I would contact the Manager, General Manager or Owner to find out what exactly their policy is on carry-in bags and why they have this policy. It is far better to get it in writing now than to go to the authorities and have the business write (or re-write) the policy in their favour later.
The policy on bags could be a safety concern (firearms, explosives, alcohol), that a bag may take-up a second seat, or that you may bring in your own food and not use their snack bar?
I do agree that some women I know have purses so big that I could camp out of them for a weekend!
Please keep us in the loop,
Mike