The thing is, culture influences infrastructure, but the reverse is also true. Bikes in the Netherlands are a way of life partly because it's very safe to bike to your destination there! You don't need Dutch culture to get to that point, look at Vancouver: https://youtu.be/N9JHfFutvik
You're right that at the moment, bikes in the US are mostly considered to be recreational, and as a result they're not treated seriously as transportation. But I think people will get to where they're going however is most convenient, and as a result we can get more people cycling by making it more convenient.
(You can count me as one of those people; I have little interest in cycling for recreation, but I would absolutely bike around the city if it were safer. Given the limited reach of our public transit, it would honestly be the quickest way to get where I need to go most of the time.)
Not to mention in New York, there's already significant risks that come with biking/scootering. You always always have to share the road for at least some part of the trip and are constantly at risk of car doors, pedestrians and ironically, really fast e-bikes. I know that during the summer the benefits outweigh the risks, at least during pandemic. During the winter with ice and snow? Hell no.