It may have only been effective in the early war, and it may have been exaggerated by propaganda, but during the Polish and French campaign the psychological effect of this aircraft was real, and, it was a really good dive bomber. Its signified a new kind of war that the enemy really hadn't figured out yet and it did terrify them.
The beginning of the end of the Stukas aura was in the Battle Of Britain. But the airplane still went on to blow up a lot of warships and it flew well in Africa.
I imagine by '43 each side was so freaked out over Jabos and dive bombers that a siren was useless cause everyone was watching the sky so much.