When I worked at a certain red Mobile operator, We did something similar to what is described in this article. A few times a year the teams got together separately and listed down all the things we could see that needed doing, and aligned them to the strategy and direction of the department and business. I quite liked it.

The final image looks quite similar to the first image (what they were trying to avoid). The graphic makes it hard to see by representing connections with circular arrows but it's still mostly hierarchical with just a few extra sideways connections.