It's not only about preventing accidents (but I do believe it prevents some to attempt answering your question).

It's also about signaling to someone that they might be doing something wrong or they might not be paying attention. For pedestrians it takes significantly less time and distance to stop, for cars, trams, and bicycles, it takes longer.

It happens all the time that pedestrians don't know the customs of a country, they don't recognize bike lines... in that case the cyclists do not need to pump the breaks anytime a clueless tourist gets in front of them... they can ring the bell, signaling:

"yo, it's not how we do it here, please watch out, I'm coming full speed and you are in the wrong, so please look up from your phone and stop right there".

I also had the luck to meet some people thinking they can be on their phone while cycling, drifting into my lane, etc... In that case, a bell is also adequate

"hey, please stop writing a text message while you are on your bike blazing through the city, you are driving as if you were drunk, pay attention please and stop multitasking (you moron)"

If nothing works to change their behavior, of course I'll try my best and hit the brakes safely, but I'd prefer they learned how to move around in the city safely.

My experiences on a motorcycle tell me that if you feel the need to honk you should be focusing on braking and evasive maneuvers instead.

The choice between between teaching some midwit the law and going home in one piece seems crystal clear to me.

In a couple of years of riding I think the horn would have very slightly helped maybe... once or twice. If the other guy would have heard it at all which is doubtful.

Phones? I've seen cyclists using laptops. Some of the most oblivious and entitled vehicle operators on the road.