The US public library system is very big. There are over 17,000 libraries and that doesn't include the almost 100,000 libraries that are in schools.
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.
Going by land area isn't a great metric, since the US has a great deal of unpopulated or sparsely populated space. Per capita might be better, but not by much. But if you go "per city," the US has around 19,000 incorporated areas. So 17k libraries to 19k incorporated areas (cities, towns, villages, designated census areas, etc.), might be better metric.
There's a town near me that has a population of 1100 and a nice small library. And there's state-wide interlibrary loan, so small-town libraries can get you anything the bigger ones have.
I guess one needs to consider the US is geographically much larger and most land doesn't actually contain people. Considering the density is wiser, but even still. Libraries per occupied area still isn't a good metric. There is no good metric.
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.
IMO the most important metric is "what percentage of kids can walk to a library without asking anybody".
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.
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.
Can I walk a mile? Yes. Can I walk a mile from my house? Not safely.
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.
In the United States (in 2020[1]), 100% of the population lived within 5 miles (8 km) of a local public library, with 99.1% of people living within 1 mile (1.6 km). That seems good enough to me.
Could your whole village walk to a library in 5 minutes?
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?
There's 3 smaller daughter-libraries in nearby villages. I'd say 20 minutes walk to the nearest library for everybody in the whole gmina is realistic. Less if you include school libraries (but they suck).
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.
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.