Perhaps the reason that they did not want people making noise that might scare the horses was that it would be unfair to the competitor if noise from the peanut gallery caused the horse to spook or become tense. It is not necessarily because they thought the rider would be unable to handle a spook.
I’ve been in competition when the wind made a cloth on the judge’s table billow and flap, spooking my horse. I handled the spook with no trouble, and it did not indicate bad training of the horse. I still lost 2 points for being off course. Show organizers can’t control natural phenomenon like the wind, but they should control extraneous noise from spectators.
I read somewhere that the reason calvary units had buglers was that by instinct horses did not naturally want to charge forward into gunfire or even another herd of horses charging at them, so they put the buglers behind the first ranks of calvary and made a lot of noise to scare them forward. I have no idea whether that is true if not.