Except for the drastically increased amount of water usage. The cost is negligible to run the dishwasher compared to the additional hot water usage.

That is a fair point, although I wonder how long this will hold true considering the ever increasing prevalence of heatpumps, sun-boilers, and other such equipment.

Stuff you should know did an episode on dishwashers and I believe if you washed your dishes for a minute, you've already used more water than a dishwasher. It was pretty mindblowing. They did, though, go through some studies that made it seem that dishwashers were too sterile and getting a little leftover or germ from your handwashed plates was better for your immune system.

There is an opportunity cost. Time spent washing dishes means time not doing something more productive.

That is precisely why you should let your $0/hr spawn pick up this menial task rather than doing it yourself - assuming your time is worth more than theirs, obviously :)

If your spawn is only worth $0/hr., they won’t have the capacity to handle it. If they are worth anything more, they would be more productive elsewhere. The income they produce for you will more than pay any dishwasher costs.