I think one thing that's needed to establish a culture of written communication is getting rid of any cultural elements that allow people to use the avoidance of reading and writing as an expression of power. You can frequently determine the balance of power between any two people in an organization by seeing which one has to read and prepare organized documents and presentations, and which one can simply speak and be spoken to. People want to paint pictures of themselves as being able to synthesize knowledge and ideas instantly, utter commands in real time and see them turned into action. In the other direction, they have no time for reading - you must request an audience with them and survive their real-time verbal sparring and probing questions to have your ideas received and considered.
My other musing on this is that I've always wondered if there would be value in teams establishing an internship or low/mid level position for a technical writer to serve as a team librarian. "Easy to search" is good, but "search" itself is not sufficient for many situations - what you need is a person who can answer questions while taking context into account. If I was running a technical team, I'd love to experiment with hiring someone whose primary accountability is answering everyone else's questions, not generating output. In the same way that a good dev needs to organize their workspace and build tools/scripts to be successful, this person will end up organizing the team's information to better accomplish their job.