The coaches tell you that because they're (mostly) talking to new riders and as you say working the horn isn't going to make a material difference and is bottom priority and ultimately clutters the mind of a new rider trying to deal with the situation.
After say 5+ years of riding bikes the braking/accelerating/turning as you say is instinct and the conscious part of the mind has plenty of bandwidth left to honk the horn :)
Totally. 5 years of smart, conscious riding will definitely give you that bandwidth, but I've also met people who've been riding twenty years tell me they "had to lay 'er down" in an accident as if it was the result of a planned maneuver and not a fistful of front brake as they shat their pants. Imo it doesn't matter how long you've been riding if you don't make the effort to hone the right instincts for when shit hits the fan.
After say 5+ years of riding bikes the braking/accelerating/turning as you say is instinct and the conscious part of the mind has plenty of bandwidth left to honk the horn :)