I love this metaphor, Fabien!
I also have observed that in planning and slicing is where problems, and ego discussions start. And amazingly, the lower is the technical skill of some of the actors, the deeper they want the technical design.
Yet, after years (decades) in the software development world, I have seen that business slicing is by far the best strategy.
And thanks a lot! I put a lot of sweat in it :-)