My understanding is that there is an ongoing debate between historical weapons experts and enthusiasts on the one side and modern sport archers on the other about whether the "one true side to shoot off of" thing is historic or a modern invention, but that the sport archer argument mostly consists of overstating the necessity of doing it the one true way, and then inferring that people absolutely must have therefore always done it that one true way, and that all the depictions of it done otherwise in historical art must have been done by people who didn't understand archery.
Yet at the same time there have been many instances of a consensus about how weapons historically worked developing amongst historians based on sources and inference that modern experiments involving actually trying to use said weapons have cast severe doubt on, so the modern sport archer's claim that "the art is wrong" is not as absurd as it may seem to a historian's ear. But ultimately, in this case, shooting from one side of the bow just doesn't seem to be so advantageous over the other, with practice, in all situations. It seems it is easier to aim accurately on the side primarily used today which makes sense for a target sport, but one can potentially nock and fire arrows faster the other way, which may make more sense for firing volleys or for a hunter trying to hit a quarry that is not going to politely stand still like a target.