I have thought of this. What you are seeing in the video is simply blowing compressed air into the rotating blower vanes against the flow. This is very inefficient.
What I have in mind is to build a close fitting housing around the rotor with ports lining up with every other blower vane and closing off the vanes in between with circular pieces of metal of the same radius as the rotor. The blower would need to have an even number of vanes. The siren would then be self powered and totally motor driven. A horn could then be added to each port for added output. It would be important that the horns would be large enough to have a cutoff frequency at least as low as the tone it would produce at maximum RPM. One way to ensure that the cutoff frequency of the horns would be low enough is to have horns tilted from the ports as in the American Signal Cyclone.
I believe a "Hoover" siren would make for a rather impressive DIY project and serve as a great burglar alarm.
The most overlooked opportunities are in the learning of and improvement in old technologies.
Richard Weisenberger