Announced to whom? Only ever to the handling agent, surely, and even that only sometimes? Never to ATC unless requested in an emergency and never, never ever to the passengers - or does the OP seem to suggest this? You'd no more tell that to pax than tell them the fuel burn or take off distances. There are wires crossed here, this is just not something that happens.
By informing all the passengers, more people will know that figure and therefore 'Someone' will be able to cascade that info to the services/rescuers.
No one , but no one tells anything to pax on that basis. Utter dreamland!