This is literally what I did as a VP Eng. I let the teams drive the improvements and kept my role to a) ask questions to help the team identify areas of improvement and b) help implement the changes when necessary. The result was that I had many teams with fairly different processes, definitions of ready & done, etc. but that was the whole point. It's all about what helps the team work best, and ownership of the process along with the result goes a long way.