A laundry washtub is not the only way to dispose of waste water. My waste water hose goes into a pipe under the laundry basin.
I lived in Germany for a couple of years. It was very common to see a washing machine in the kitchen (front loader under the kitchen bench). The other popular location was the bathroom. There was no second laundry basin. The waste water hose is connected to wherever the waste water is supposed to go.
Dishwashers don’t feed their waste water into the kitchen sink.