The whole is greater than the sum of its parts. Often you need to disregard the detail and minutiae of existing processes to set a better course. The goal is not to avoid short or even medium term pain or even unintended consequences at a department level, but rather to steer the company in a new direction. Processes should adapt or be thrown out to achieve the new direction.

This is not too dissimilar when you realize a software architecture is holding you back. You don’t try to “save” all the existing functions, modules, layers, etc. but instead are happy to discard or replace them given your top-down vantage point of the system and where it needs to head.