A Stall horn will tell you, you are (close to) no longer flying, but actually falling.
Since this is of paramount importance for every airplane, it will sound until recovery is completed. Often it is only the silencing of the stall horn that can give a pilot certainty about that. Sometimes even this is ignored, because pilots treat it as just as alarming as any other device, which it isn't. Gear malfunction, terrain alert, traffic alert, burning engine, a hijacker holding you at gun point, all these things are of minor importance compared to a stall.
As dictated by law, a stall horn works on every winged aircraft, even if all power is lost and all other instruments are dead. (EDIT: this is not correct. It should be, but it ain't. See comments)
A winged aircraft with a continuously sounding stall horn is in the process of crashing. It is not going there, it is there. Its falling, like a brick.
Tell me, why would anybody in his right mind ever want to even just be able to shut that down?