Bikes are also healthy for people, and they're certainly more space-efficient than cars. Oh, and they're vastly less expensive for the city as well; building subways is enormously capital intensive, and buses have high ongoing operating expenses. Good quality bike infrastructure isn't exactly cheap...except that compared to high quality car or transit infrastructure, yeah it is relatively cheap.
So, altogether, replacing car space with bike space makes a ton of sense, especially for a city as dense as NYC. Sure, bus and subways improvements should happen too, but there's so much car space that's wasteful, and bike stuff is so cheap, that it's really low hanging fruit. No good reason not to develop it.
Building bike lanes can also be used for scooters and other kinds of non-auto transport.
Finally, mass transit is an order of magnitude more difficult to plan and implement, as effective MT needs to not only coexist with vehicles, but pre-empt them at intersections. Otherwise, they're slow and no one uses them.
Most cities in the US will never have a subway, so the only option is light-rail or protected bus lanes.
I do think there is overlap in bike lane interest and public transit. TransAlt's mission, for example, "is to reclaim New York City's streets from the automobile and advocate for better bicycling, walking, and public transit for all New Yorkers." I'm pretty sure they were helpers on the 14th St bus way pilot.