Just to be clear
There was a whole separate tub used for dish washing, which of course was sold as an add-on to washer. While that didn't always calm the "ick" factor for some, in theory dirty dishes and soiled laundry never were washing in same tub.
When you think about it that second tub for washing dishes wasn't always so convenient.
When not in use one had to find a place for storing the thing. Also unless it was left in washer (in which case a place had to be found to store laundry tub), you couldn't load dishes after each meal and run machine later that day.