In short, washing yeast is a way that will allow you to store it for a short while and reuse the yeast. Yes, you can pitch onto a fresh yeast cake but in almost every instance this is over pitching onto stressed yeast. (Bob wrote a HUGE article about why we should not pitch onto a cake.) Building a starter from washed yeast is generally considered the "right way".
I have actually chosen to start a frozen yeast bank. I am just finalizing the area and equipment.