Why didn't the Buddha write a book outlining his teaching? Perhaps with the exception of Laozi, most sages, founders of religion, &amp; great thinkers from virtuous tradition do not leave us books authored directly by them. In most cases what we have is books written by their followers or commentators.
Some did say why they don't want to write. Did the Buddha say why he prefers oral transmission?

Thank you for the responses and historical references, it's hard to believe that the cause for not writing a book to be lack of written script or writing material, India wasn't that lacking, they even had some intriguing advanced mathematics compare to other civilization and writing did exist by the end of the Vedic period which aligns with Buddha time... But perhaps, as @Andrei noted the oral tradition was more advanced and the preferred method.
I asked because I thought maybe the Buddha, the same as other thinkers, saw writing as an incorrect way to transmit his message. For example, Socrates compared writing to dead painting as quoted below, but his view is not directly applicable to Buddhism and in a wider sense to Vedic oral transmission, because the method (i.e the oral transmission) is not about dialectic rather repeating the exact word and phrase. So, for an external observer is an excellent candidate for writing.

The painter’s products stand before us as though they were alive. But
if you question them, they maintain a most majestic silence. It is the
same with written words. They seem to talk to you as though they were
intelligent, but if you ask them anything about what they say from a
desire to be instructed they go on telling just the same thing forever

.
The four nikayas do not mention &quot;writing&quot;. However they do mention &quot;reciting&quot; many times. One mention, in particular is quite interesting:

AN8.20:6.4: It’s impossible, mendicants, it can’t happen that a Realized One could recite the monastic code in an impure assembly.

In another sutta, the Buddha instructs:

DN29:17.1: So, Cunda, you should all come together and recite in concert, without disputing, those things I have taught you from my direct knowledge, comparing meaning with meaning and phrasing with phrasing, so that this spiritual path may last for a long time. That would be for the welfare and happiness of the people, for the benefit, welfare, and happiness of gods and humans.

What is notable about these and many other quotes is the amount of care mandated in transmitting the Dhamma. The transmission of the Dhamma goes beyond mere written duplication via Gutenberg printing press or mindless scribe. The transmission of the Dhamma requires transmission of pure understanding, with care taken to ensure the meaning and phrasing of what is spoken and heard. Specifically, what is required is:

AN2.126:1.3: The words of another and proper attention.

In my own experience, I have found that hearing, reciting and discussing the Dhamma to be far more powerful and effective than mere reading. I have found the eye to be fickle in its grasping as it flits from here to there seeing what it wants to see as it skims the written word. In contrast, hearing and reciting and discussing demand far more attentiveness. And although the Dhamma is available for reading, I myself study the Dhamma by listening, reciting and discussing. The difference in understanding is remarkable. I cannot say what the Buddha intended. All I can say is that reading is too superficial for me. Instead, I rely on hearing, memorizing and speaking the Dhamma in concert. And that oral tradition does indeed work for me. The oral tradition facilitates proper attention.