There are TWO theories of "fire," and which one is better depends on what the battle conditions are and what the general is trying to accomplish.
Admittedly, the examples below are with muskets, not archery, but you'll get the idea.
One theory of fire is "fire at will" (or what a computer programmer might call "free format.") That works best in a "broken" battle on broken ground. The classic example from the American Revolution is "Lexington and Concord."
At the battle of Quebec, on the other hand, Britain's General Wolfe defeated France's General Montcalm. The latter allowed his troops to fire at will, while Wolfe had his troops fire "in sync" followed by a bayonet charge. The advantage of "in sync" is the shock value, especially when followed by a bayonet charge. Without such factors, "fire at will" (aim, and use top speed), is probably better.
EUROPEAN archers tended to fire "in sync." But at one notable 1754 battle in what later became the United States, a mixed force of British and "American" soldiers under Britain's General Braddock was defeated by French (with muskets) and Indians (with bow and arrow) "firing at will" from ambush. The losing and dying general, Braddock, gave the "props" to a brave and capable "rookie" officer named George Washington, who had warned that synchonized fire wouldn't work in "America"--"and the rest is history."