iirc most motorcycle safety coaches will advise that the horn is usually the last thing you should be thinking about in a dangerous situation. It's a great tool for proactively getting someone's attention, but in an emergency the motorcyclist should focus all of their energy on maneuvering to safety regardless of how the car behaves. Motorcycles are maneuverable enough that generally if you have time to honk you have time to be proactive about your own safety rather than rely on the driver hearing you.
If you're able to focus on both that's great but most riders fall back onto instinct and that instinct should be braking, accelerating, or turning rather than honking.
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.
If you're able to focus on both that's great but most riders fall back onto instinct and that instinct should be braking, accelerating, or turning rather than honking.