They don't necessarily know "That's the tornado warning siren" (as opposed to some other siren), though. More important when there's multiple possible alerts, of course.
Many of them are old. They do break fairly often, as is the general way of electromechanical things that live outdoors in every kind of weather.
And if having twice as many for redundancy were a viable option financially, they'd already be installed. Doubling the density would be a good thing, but this shit is expensive.
One county near me in Ohio does weekly tests, and conducts hands-on PM checks every spring and every fall for every siren.
(Background: I have been personally involved with these PM checks, the sale and commissioning of new sirens, and implementing the back-end controls for these sirens.
I think I've personally done everything with them but plant the poles in the ground.)