I completely disagree, this is just another level of safety.

If everything went perfectly everytime we wouldn't need any safety equipment, but things aren't always perfect.

Regular alarm sounds already do that, because above 1kHz or so it's the cushioning in the device that does the majority of the cancelling. There's a dip in effectiveness before that because to cancel noise effectively it's best to have a latency lower than a quarter of the wave's period.

Also ANC works best on wide-spectrum sounds, so any kind of siren or the cries of a child will go through, as the spectrum is a series of narrow peaks.

> Draw a line, say this is for bicycles, pedestrians and cars have no business here, and bikes have no business being on any other lane as long as these exist.

This is the reality in many cities, if it weren't for the hopefully not surprising fact that people don't always obey traffic laws perfectly.

A horn or bell is mostly for telling other people "hey I'm here, stay out of my way and dont suddenly cross into my path"

My opinion as a cyclist is that I should basically only be using my bell on pedestrians when the pedestrians are wandering onto the bike lane. If im cycling through a shared space, I find it extremely rude to ring the bell, because it feels like I'm telling people to get out of my way, but they have just as much right to a shared path as I do. Some cyclists ring their bells because they're worried a pedestrian might suddenly turn into their path, but I think if one is concerned about that, it's a sign youre cycling too fast, and should just slow down.

With cars, I will sometimes proactively ring my bell at them if I think they're not sufficiently aware enough of me though.

> Do horns and bells really prevent accidents?

They absolutely do, for indirect reasons:

> Generally it's a lot easier just to press the brake

Maybe easier, but it hardly seems fair, nor realistic.

With a bit of experience, you can tell when pedestrians are likely to stumble onto the bike lane without looking. Then you have two choices: Significantly reduce your speed, or ring your bell first and only reduce speed if they still haven't noticed the oncoming bike.

If you only reduce speed, you'll be traveling at a very low average speed, and time is money (especially for bike delivery workers, but I also hate having to sharply decelerate for people glued to their screen or otherwise completely unaware of their surroundings even if I'm not in a rush), so you can take a guess as to whether "just reducing your speed" is practicable.

Bicycle bells are mostly for warning pedestrians when approaching from behind and passing on shared-use trails. I ride on shared infrastructure and cannot afford to build new infrastructure when my town will not. Not warning a pedestrian when approaching from behind introduces the possibility of collision if the pedestrian makes a sudden change in his walking course. I typically use this etiquette:

Passing a single pedestrian or runner on a quiet day: no bell, coasting for a short bit with a loud free hub (the rotating ratchet element on the rear wheel) alerts the pedestrian to my presence.

Passing a runner: normal ring from a distance so they have knowledge that the bicycle is passing

Passing a cyclist: one loud ring from a distance

Passing a pedestrian walking a dog: two loud rings, one far, one close, so that the pedestrian is aware of the approaching bicycle and he can prevent his dog from running at me/colliding. Many dogs do seem to enjoy a bicycle chase.

Antisocial pedestrians (i.e., walking side-by-side such as to be blocking the path in both directions, preventing the bicyclist from passing): several loud rings of the bell until the antisocial activity has abated. Announcements in my local tongue (not English) that they impede the flow of traffic.

I've been a cyclist in SF and in Amsterdam, both for many years.

In SF I used my bell much more aggressively. It was mainly for cars, if I'm in or entering their blind spot and my spidey sense tells me they are considering an action that places me in danger. For example, we all know when driving when the car in front of us is thinking about merging, even before they indicate (often I feel like I know before they do). I also used it for pedestrians stepping out into the street who are maybe looking past me for oncoming cars but somehow don't see me, or when approaching 'blind' situations like a sharp corner, a driver pulling out of a driveway but there is a tree between us, delivery drivers stepping out from their truck, etc. I can't say how many accidents have been prevented (the person may have eventually looked and seen me), but I can say that my bell has triggered people to look and see me earlier than they were going to had I not rang it.

In Amsterdam my bell is used much more sparingly. It's mostly for tourists stepping into (or considering stepping into) the bike lane. If they are already in the bike lane, I almost always prefer just to slow down a bit and dodge them, as ringing the bell often triggers a deer-caught-in-headlight moment or erratic behavior, which increases the chance of an accident or that I have to come to a full stop. The other situation is to express dissatisfaction at cars blocking bike lanes, cars/bikes not yielding, drivers blocking intersections, or other dangerous behavior. This isn't preventing an accident but I'd argue it is still important, as social control affects how often we make bad decisions. Outside the city I also use my bell to let other cyclists know I'm passing.

So yeah, I'd say bells prevent accidents, but obviously not as well as good biking infrastructure, where pedestrians, bikes, and cars have clear separate spaces, and visibility of cyclists to drivers is high.