They're probably not allowed to do that anymore for health & safety reasons
When did the tradition of raising the cup to the crowd begin? When the winning captain collects the cup from the queen (or whoever) they always turn around and lift it in the air. I remember seeing some footage from 1946 of Derby County captain Jack Nicolas collecting the cup (from King George VI?), then proceeding away and back down the stairs towards the pitch. It looked very strange that he didn't raise the trophy towards the crowd