Partly because in most restaurants, machines actually wash the dishes. You don't need some cheap laborer with 8 kids going to school at $10,000 each per year who makes $4 an hour and can't afford health insurance or to pay his own doctor bills for his family.
I washed dishes for Farrell's Ice Cream in high school. Someone still has to rinse and rack the dishes before putting them through the wash/sanitize machine. Once complete, someone has to put the clean dishes where they are accessible to the cook/wait/fountain staff. That someone is the dishwasher.
I got tired of washing dishes pretty fast. It took a whole two weeks to pass all the written tests and practicals to switch to the cook position. Another couple of weeks to learn all the fountain stuff. It was on Ok job for a high school senior to cover costs for the prom, class ring and annual.