Sounds like you had an exceptional experience, having seen more crashes in one week than I see in years of living here. And I promise you, I spend a lot more time on foot and on bike in the city than you do.
Regardless, are you really saying that "bikes are simply better at point-to-point transportation" for most people in Manhatten? Because that's absurd.
And yes, I would say it's best for most people in Manhattan. It would be even better if we build more bike lanes and get more cars off the road.