To build a library close enough to most American kids that they could walk to it would likely be infeasible, because so many people live places that are simply not walkable at all.
There's a road I would have to walk down to get to anything that isn't on my street. One lane each way, no shoulders, no sidewalks, and very poor visibility of oncoming traffic due to an inconveniently placed hill.
The nearest public library to my childhood home was 2.2 miles; I would occasionally bike to it before I had a car, but it involved crossing one major street.