UAL tried this back in the Shuttle days and some enterprising ****ed off lawyer sued UAL. Back then they put restrictor plates on the x-ray bag screening machines. Anything that wouldn't go through, had to be checked. The suit said the security check points had nothing to do with airline policy. That was a security/safety and FAA matter not airline policy.
Off came the restrictors. Of course that was before we charged for bags. I'm guessing we can't make money by flying people and selling tickets, we can make money by checking bags. Here we go again....