Translation:There are ten books.
Yup, it's to provide context clues when the word "book" isn't explicitly stated (usually it isn't). It's actually pretty useful since it conveys way more info than English... for example, if you were in a bookstore that also had other things than books for sale, you can't just say "I want 7" since it wouldn't be clear enough and you could end up with 7 pencils or whatever... on the other hand, in Japanese you can say "I want 7" and end up with 7 books since the number came with a mutually understood context clue.
How in the world do you get that it would be more useful than just specifically saying "books"? Especially when most of these counters apply to many different items with similar characteristics. In some places it may be a little more convenient. In a lot of others it seems it would just be confusing when the counter doesnt make clear which item you mean, plus an added hassle to try and point out what you meant in the first place.
An interesting theory, but I think you're mixing something up. The counter for cylindrical objects is the same as word for 'book': 本 （ほん）. This includes rolled up things like film, possibly because books used to be scrolls. It's unrelated to the counter for flat objects (冊) though, which is what we count books with today.
Serious answer: about a dozen or a whole lot more, depending on what you think of as counters.
Take the lists on https://en.wikipedia.org/wiki/Japanese_counter_word for example. They include things like seconds, minutes, hours. Technically I suppose those are counters, but I assume you meant counters that are 'only' in the Japanese language. Otherwise grams, centimeters and all those would be counters too.