You've heard about a pedestrian who you don't even know had an accident and determine its too unsafe.
Meanwhile I personally know multiple people who died, mangled in a car after an accident. I know multiple people who have survived but were in bad accidents where at least one person was injured. I know multiple people who were pedestrians and cyclists who were properly using the streets and were hit by cars requiring hospital visits, and indirectly know of several people who have died being legally in the right cycling on the streets.
You're way more likely to be seriously harmed or killed even just being around a car than you are riding a train or subway.
Inside Manhattan this is almost certainly true. In a modern car you're going to walk away from almost all crashes under about 40 mph.