The access point has to send some broadcast packets into the air, otherwise the network wouldn't work. As long as the wireless interface isn't congested, there is little reason not to send them all. In case of congestion it has to decide which packets goes through and which are dropped. At that point it may handle broadcast packets differently from other packets.
A switch has to transmit a broadcast packet on all ports except from the one it was received on. An access point should not have to send the packet once to every device associated with that access point. Instead it should be sufficient to send it once and have all devices simultaneously receive the packet being broadcast just once.