Many of the bike lanes in NYC are nothing but a stripe of paint along the side of a single-lane road, whose curbs are lined with parked cars. Cars double-parking for loading, etc will inevitably either block the bike lane or block the auto lane, causing cars to swerve into the bike lane.
The obvious solution is to remove the on-street car parking on at least one side of any street that hosts a bike lane, and use the space for a separated bike route with a protective barrier. Unfortunately I doubt it's politically feasible at this time. There's plenty of resistance to bike lanes already; reducing the street parking would be seen as an undue hardship on the middle class.
I do feel things will change over time though -- I know several New Yorkers who used to have cars but now, in the age of car/bike sharing and app-enabled car services, no longer own one.
eg, https://www.google.com/maps/@40.7784195,-73.9470116,3a,75y,2...