Here's my understanding of one of the winning behaviors of Toyota, namely copying and improving on kaizen ideas that work. We'll call this yokoten since it's more precise than "copy" or "horizontal deployment" or "sideways expansion".
It's not a vertical (top-down) requirement to copy as Intel might deploy it in their "copy exactly" model. It's not a "best practices" or benchmarking approach per se. Yokoten is horizonal, or more peer-to-peer, with the expectation that people go see for themselves and learn how another area did kaizen. In yokoten at Toyota there is an expectation that copying a good idea will be followed by some added kaizen to that idea.
One thing that we often hear is that communication and exchange of accurate information horizontally in an organization is important. These would be cross-functional exchanges of information or across business units and value streams that may not have formal channels of communication.
Rather than waiting for the kaizen information to go up the chain of command where it can be sent back down to another area to copy or learn from, as I understand it Toyota people are encouraged to go see for themselves, and return to their own area to add their own wisdom and ideas to the knowledge they gained.
The role of the senior managers is to make people aware of the existence of these good kaizen examples so that they can go see for themselves, gain the knowledge and improve upon it further. Simply telling subordinates to copy it may be kaizen of a sort but it would not serve the second important aspect of the Toyota Production System, the respect for and development of people.