Electric cars still make noise: the wind, the tires, and for trucks the cargo can too sometimes. It's just that they would make considerably
less noise.
Blind people usually don't simply jaywalk a crowded street, they cross at the lights. And you'd still be able to hear moving cars.
I don't think phones ring because we rely on our ears in times of danger. It's because hearing is one of the senses that doesn't require exclusive focus (you would not want to stare at your phone all day until it starts blinking, although in some offices they do). Smell and taste wouldn't be alternatives for obvious reasons, but feel could be, and in fact phones can vibrate. Some wrist alarm clocks do too. And fire alarms are nothing we're exposed to every hour of the day.
I acknowledge that the fact that cars are pretty loud could be helpful in reducing accidents. But apparently your theory has a flaw, or else no one would ever get hit by a car. Now, one could say that more people would get hit by cars if all cars were super-silent, but my original point was that this is just because we're not (yet) used to more silent cars. I think pedestrians would change their behavior and get used to them.
For people living on highly frequented roads, continous noise can become a very stressful factor. It drastically reduces quality of life and can negatively affect your psychological and physical health. That doesn't mean that every person living on a busy street gets sick. But I would still argue in favor of reducing noise where possible, and more silent engines could be one factor.