Commuted for years, also Brooklyn to Manhattan about the same distance. Had to stop due to back issues but I can echo all the OP’s benefits.
Biking is somewhat dangerous in NYC, and every other American city. I agree with OP that NYC drivers are generally very good though. It’s the bikers responsibility to bike as though drivers are -trying- to kill you. First heard that advice when riding motorcycles and it’s stuck with me.
I’ve been in a few spills on my bike. A big one with a pedestrian who strolled into a protected high speed path at prospect park. Another one with an invisible pothole at night in park slope. The last was pure user error, riding tipsy from my local bar home :)
Generally, riding in nyc, like walking in nyc, is a unique skill set. You really MUST be able to do things like look behind you while riding, and it’s quite helpful to be able to accelerate to near traffic speeds. Of course you must assume any car door can open at any time. Route planning also goes a long way; it’s usually worthwhile to take a slightly longer route to stay on smooth streets or protected lanes. Extra wide one-way streets in Brooklyn are generally quite good for cyclists as well.