My city (Seattle, a pretty large US city) has 27 public libraries. I only live a few blocks from the closest one but could fairly easily walk to at least 2 more.
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.
There are probably even smaller towns, but I know Flatonia has one because I've been there.
What's more important is the qualitative offerings and impact:
1. Spectrum of a. most common services and collections offered everywhere to b. the most comprehensive of those offered by a specific library.
2. What people can do at them: read, research subjects, borrow things, accomplish tasks, host meetings, etc.
This is very hard to measure and not something a business person running the government "like a business" would understand.
But nowadays people have internet, so I guess it's not THAT important anymore. The ideal library is just a website that lets you download pirated ebooks for free.
The utility of the brick-and-mortar is that some/(many by state) libraries include services and physical items that can be checked out besides media. Plus, besides free Wi-Fi and meeting rooms, it's a non-consumption location to exist in a physical public space. There aren't many more free spaces in America. And, there are millions of people who can't afford internet, a tablet, a computer, or have a place for books. Millions of books and historical local newspapers don't exist in electronic form!
But no, really, (most of) America is truly unwalkable for almost any activity.
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.
[1] https://www.gc.cuny.edu/center-urban-research/research-proje...
Regardless of population density, villages/towns/settlements/cities tend to span a mile or more, not one acre with 1-1000 people surrounded by non-residential space.
How many books were in that library that served 500 people?
I had no idea how many books, checked right now and apparently it's 32 000. It's not really serving 500 people, it's got 1100 regular readers. Which means people are going there from other villages.
It also has all the multimedia stuff, audiobooks, internet access, printers, etc.