Entering a public restroom, I found a toilet with the thing you flush your toilet with (I don't know what you call it) on the right side in the perspective of a male who is peeing :). Well, it would have been convenient if I were a right-handed male who is merely peeing. However, that restroom is for both sexes, and not everyone is right-handed, nor not everyone take a benefit from the position of that thing.
Statistically speaking, the majority of toilet users will find that particular location not helpful. The great majority of people is right-handed. And all females, in general, take care of their biological business sitting. Males take their poop sitting. So in general and in conclusion, only males who are right handed and peeing are the ones benefiting from the particular position. Traditional position of flushing thingy is good for the majority and I think it should stay that way.
Jin Woo Won
An undergrad at Columbia University, studying Computer Science and in particular artificial intelligence.