I actually don't recall ever seeing a human do dishes that way except on TV. I'm also not sure that it saves water if you are filling the sink and then still using water to rinse the dishes, at least as compared with my method.

Finally, there has been very few times where it has been necessary for me to use hot water instead of cold. Unless I had burned the food, almost everything will come off after a good soak and scrub, even in cold water.