No I'm not. I don't care how you heat your water. I'm saying you (should) heat it either way, and you use more of it when hand-washing so if you do pay to heat it, you pay more by handwashing.
And in your case, you use more water because you hand-wash, than you would if you used a dishwasher. You use slightly less energy because of the pump but also a lot more of your time, so... obviously how you relatively value those different things is up to you.
You're a bit all over the shop in that answer.
Our concern here, and that of many people in the area, is total water usage per household - and to a large degree water usage for washing, showers, and toilets is a small fraction of the total usage - and one that can be ignored as most people have grey water capture (as do well planned and infrastructured cities).
Water used inside the house runs out to water food, shade, animals, etc. and that use can be deducted from the water that is required for those uses.
Energy is no great cost, it comes from the sun - both as electricity via panels and directly as heat via solar hot water systems.