A very interesting question! Thanks for raising it and giving us something to think about.
Is it possible that the Buddha just did not think there was a great deal of information that had to be (or could be) transmitted through the medium of standardized linguistic formulations in order for the dhamma to be preserved and propagated? After all, of the eight parts of the Noble Eightfold Path, only right view arguably involves the storing of propositional knowledge in standardized formulations, and that body of statements can be regarded as relatively limited: some statements about the nature and causes of suffering, and about the path leading to the cessation of suffering. For the most part, when the Buddha explains right view, it consists in having the right mental orientation toward the world and what is of most value in it, not having mastered any body of doctrine.
In the Buddha’s context, no knowledge was spread by books, the internet, or other forms of writing, but was passed on person to person. Perhaps the Buddha’s intention was that the future teachers of the dhamma would be realized arahants, and the students would be instructed by those arahants on the rules of the discipline, the nature of the ultimate goal of the holy life, and the practices leading to the realization of the goal. These teachings about the dhamma would flow directly from the realized state of the arahant, known by the arahant’s own direct knowledge, in whatever way the arahant found to be a skillful means of communicating the content of that state and the path leading to it.
The Buddha often seems to suggest that the lives and minds of Brahmans were so cloyed with mechanically reproduced precepts and practices, and mountains of vedic learning, that they had no space left within to liberate themselves. Maybe he was concerned about not recreating similar systems of overabundant discursive teachings and slavish indoctrination.
Like a master musician, the Buddha was primarily a teacher of practices to apprentice-followers, who he expected would then go on to instruct others in the same practices - generally without the assistance of lengthy written tomes or extended verbal discourses. The Buddha’s practices involve mainly habits of peaceful, purified and restrained personal conduct, disciplined and respectful community living, attentive awareness to one’s actions, and energetic cultivation of deep states of mental concentration. The Buddha did give discursive teachings, but explicitly warned any discursive views gleaned from those teachings were provisional tools for passing over the floods, not something to be held onto.
All this said, there are many places in the suttas where the Buddha seems to employ a method of teaching that consists in having students memorize teachings “in brief”, and then querying them to see whether they themselves can expound the detailed meaning encapsulated in those concise, brief formulations. So maybe there was a focus on the recording of concise bits to be carried around by people who had the discernment to know what they meant.
Also, someone will have to refresh my memory about where it is to be found, but there is a passage somewhere in one of the commentaries where one of the main disciples - Maha Kassapa perhaps? - tells the Buddha that he desires to wander and spread the dhamma. Some time later, one of Kassapa’s students makes a pilgrimage to meet the Blessed One, and on meeting the student the Buddha quizzes him on his knowledge of certain discourses. Could someone please remind me where this story is found?