Well, Tim, if I have no support I should step down, shouldn't I?
The problem with your analogy is that it's not my ball. The ball belongs to the project team, not to me. The proper analogy runs more like this - "I'll step down so the project team can play with their ball using whatever rules they want".
In your analogy, if I take my ball home, the game comes to an end. Certainly that's not the case here. If I step down, the game will be played, with the same ball, just with different rules, that's all.
Now, as the saying goes, the ball is in Jerry's court...