There are several interesting issues in this.
First, I believe that if a person does not have a certain degree of inclination to serve others, washing dishes will not relax him in any case.
Thus, by doing so you are helping another and also you keep your mind occupied on one level (washing the dishes and doing it well) and on another level the mind can relax, wander, meditate.
The effective action of serving another is always positive for many.