Forcing everyone to fire in unison allows the commander to easily identify and execute shirkers, and thus increases the probability that everyone will fire. Individual arrows are also lost in the volley, and thus individual archers can have plausible deniability that they have just killed a human being.
Most military tactics are about getting the most out of an individual soldier, and "most" here is a euphemism for most violence. In Medieval times, there were very few professional soldiers - most soldiers were farmers conscripted by their villages or towns and forced to go to war. And, as has been documented throughout military history, most human beings really, really do not want to kill other human beings. Thus, in a free fire situation a conscript will generally try to do the minimum firing necessary to get home alive. This, however, doesn't match with the commander's goal of inflicting maximum casualties on the enemy. Thus most militaries would at least threaten to execute anyone who failed to perform the duty they were conscripted into.
However, to prove that one conscript out of hundreds wasn't taking shots of "opportunity" would be difficult, and increase the monitoring costs of the officers. When the monitoring costs are low, as in coordinated volley fire, an individual archer faces the very real possibility of execution if they do not fire an arrow at the appointed moment. Thus in such battle drills you will see seemingly "pointless" actions like archers holding up the arrow they are about to shoot (so that commanders can see they actually are holding an arrow to shoot) and a pause after a shot goes out (so that commanders can see they are no longer holding said arrow).
If we assume that half of archers would not fire in a free fire situation, you can see that a commander can easily double the effective damage on the enemy with good monitoring routines. However, the rates of non-firing may have been significantly higher than 50%. For example, in World War II it was well documented that only about 20% of soldiers actually fired at the enemy when in combat, which generally used small unit tactics focusing on free fire. If medieval archers were similarly averse to killing, then volley fire tactics could increase damage by 400%.