I think it works in a respectful relationship. She will clean up the dishes, just in her own time. If I can't stand them in the sink there is any easy way to fix that problem.Exactly.
Her running out of gas on the side of the rush is going to irritate her way more than it irritates him LOL.
I like your agreement, and I bet it works well for two motivated, reasonable individuals. But I can see it going way sideways if one person is a lazy bum. "It doesn't bother me that there are a pile of dishes. Maybe you should own that...."