Nope, you wouldn't. I come from a family of 6 and we didn't have a mechanical dishwasher. (Whoever was in the most trouble with mum at the time was the dishwasher.)

As of two weeks ago, I have a dishwasher. I've used it exactly once, after cooking for 5 people. I did a load of dishes in the sink by hand while it was running. I look at as a convenient place to store clean dishes, not something to wash them :)