As someone who has sat behind the wheel of an ambulance and various firetrucks, even those sirens aren't enough to get other people on the road or sidewalks to pull their collective heads out of their arses long enough to pay attention to their surroundings and get out of the way. And it is possible to over drive the sound also. But cars tend to be so well sound insulated these days that it's doubtful any bicycle siren is going to really be loud enough to get one's attention.

We finally installed a "rumbler" on some of the vehicles to assist the siren and lights to get attention. A rumbler is a large speaker installed behind the grill and aimed downwards to the ground. When you hit the switch, it would emit a very low pitched note that would literally cause the ground to rumble and quake ahead of the vehicle as you drive. They have a limited usage life, so you only used it as needed to wake someone up long enough to get them out of the way.

But I'm personally of the opinion that bicycles should carry more lighting than they do. A headlight, rear facing marker/brake/turn signal lights should be a standard requirement for new bicycles. It would increase safety for everyone.