It's their weight and balance program for the CRJ.
By not allowing full-sized carry-ons in the cabin, they can use a lower average passenger weight (which includes the weight of cabin bags) then count the gate checked bags and add a standard weight for each of them.
If they chose to allow but a carry-on and personal item into the cabin they'd have to use a higher average weight for each passenger in their calculations and, for many flights, would end up more weight restricted. These programs are common on CRJ and E145 operators.