The economy of motion issue is more than trumped by the fact that the act of flushing causes a fine mist to spread as far as 6 feet from the bowl. Those who prefer to have no sewage mist on their toothbrushes (which are presumably within range) will find it most advantageous to put down not only the seat but the lid.

And be sure to wash your hands afterward, preferably turning on the water prior to touching the toilet.