hmm... well in Arizona the license is the L-38 Contractors License... Do not know about cities not requiring one, since it is a State thing. Cities are usually required to follow and inspect using the building code which included requiring a Licensed Sign Contractor... The Cities I have dealt with in Arizona required one.
In Arizona an L-38 is:
L-38 SIGNS
Fabricate, install, repair, and service indoor or outdoor signs, displays, and sign devices attached to, or painted on a structure for the purpose of display, advertising or direction, including painting for background and decorative purposes; sign supports and accessories; flagpoles; electrical wiring directly connecting signs, displays, and sign devices to the first adequate power outlet accessible and adjacent to the sign, display, or sign device.
I think the biggest reason to carry one is, making a sign without a license means a customer does not have to pay you, and they may have the right to get a refund.