It doesn't seem like "A lot" for a country the size of US TBH.
Poland has 7541 public libraries. Which is 1 per 41 km^2, but of course big cities have many libraries, so the actual distance is larger in the countryside. But it's a number.
17000 libraries in US is like one per 580 km^2.
And yes every school has one too, there's 35 000 schools. But many of these are very small libraries that mostly carry mandatory lectures for school + some classic books. In my village the school library sucked.
I lived in a village of 500 people and had a library within 5 minute walk.