Why is sentence #4 not incorrect?

了 is the Aspect Particle (动态助词), and Modal Particle (语气助词).

We short them as the 了(1), and 了(2).

Here 了(1) is the Aspect Particle, we use this formula to express a complete sentence:
"Verb + 了(1) + Attributive (Quantity phrase/Noun/Adjective) + Object", so the correct is 我买了一本书。

But 我买了书 is incorrect indeed, it is not a complete sentence in the Chinese language, and just like there is a lack of information following that makes the listener feel that the sentence was not completed. 我买了书, that means I buy a book, but what do next?

eg, the correct one,
我买了(1)书，然后回家了(2)。 I buy a book and then I go home.
了(1) indicates the completion of an action;
了(2) used to express a tone, indicates the completion of the sentence;

Therefore,
了(1) to express the completion of the action, it can not be directly followed by the object, the object must be preceded by an attributive, which can be a quantity phrase, noun, adjective, etc.

If the following of 了(1) is a simple object, the sentence is not complete, generally to add other components after the object, can be a clause.

Another, just as mentioned by @shichutian02 below, in a certain context, if someone asks you what you buy, you can just say 我买了书, because the listener knows the precondition, he/she asked the question.

I completely agree with shichutian02's explaination about your question. Chinese is high-context language. Usually it is too haste to say one independent sentence is correct or incorrect. Put the sentence in a context, you can understand it better. In a conversation like "你买了什么？”"我买了书。”，（1）is correct. But if you say it to listener positively, it sounds like an incomplete sentence.，the listener will wait for your next part of the sentence, it is incorrect. Because the listener totally has no idea about your action, you should say the event first and then say "了“ to introduce a new information. (我买书了。我打游戏了。他有女朋友了。）That's why (4) is correct by adding "还买了水果” to make the meaning of the sentence completed. I hope this can help a little.

As a native speaker I would say 我买了书 is definitely something I as well as my Chinese friends would say in daily life. It's just that the emphasis is on "书" -- "我买了书" implies that "what I have bought is nothing else but a book", whereas a sentence like "我买了一本书" does not have such emphasis but is just stating the fact that I have bought a book. So when you are asked a question like “你买了什么？”, "我买了书" would sound perfectly fine since you want to emphasize "书".

Therefore, my explanation for why #4 is not wrong would be that by adding a second thing that you have bought you are automatically putting emphasis on these two things -- "I have bought THIS and THIS (but not THAT or THAT)". I hope this makes sense...

Also, as you can see in the grammar explanation from your book, it says “表动作完成的‘动词+了’的宾语一般是‘’数量短语+名词’’”, so the object in this structure is "usually" a number+noun but not "always" the case. This would be the best explanation I can give.

You may proceed to this link https://www.cchatty.com/l-101537 as this topic is clarified by a teacher clearly and hope it is helpful.