Keep in mind that biking isn't about traveling within a neighborhood - biking is the option for being able to travel between neighborhoods without using a car. So even if one neighborhood is walkable, bike infrastructure is necessary for anyone who wants to e.g. commute to work or bike to a friend in another area or get to a grocery store if they live far from one.

Also, and I'm not saying this is what you said, but I do get frustrated at the implications people make that if they don't see a lot of bikers in a bike lane, that means the bike lanes aren't worth it. The reality is twofold: 1) unless they're watching the lane all the time and keeping a counter, what someone sees is just anecdotes; and 2) it takes building protected bike lanes to get more people to bike - there are surveys out there showing that in cities many more people would bike if they felt the infrastructure supported it. So sure, maybe fewer people use a given bike lane for now, but once it gets connected to other bike lanes across the city, it will attract more folks to bike. You can't just put in one lane on one street and go "no one it using this, therefore the bike lane is useless" because it ignores the larger context.