Surely washing clothes by hand cuts down on energy usage :)
That may or may not be the case. It depends heavily on the energy investment for that water - how much energy went into getting it, purifying it, distributing it, and heating it. Next, consider the amount of soap you are using. A modern high efficiency washing machine uses very little soap per clothing article. Human hand washing (clothes or dishes) tend to oversoap, which is wasteful on its own, but also requires more water to rinse out. Finally, consider the energy used for drying the clothes. Hand-washing is usually associated with line-drying, but you might still be using an electric dryer.
If you are hunched over a creek, scrubbing your clothes on a rock with freezing, chapped hands, followed by line-drying in the sun, then you clearly are doing better than the status quo. But if you are filling a great big tub multiple times (wash, rinse, etc.), with water that came from oil-fired desalination plants and heated to a balmy 30 C, then using an electric dryer on high, "hand washing" will clearly be more energy-intensive.