First, as far as we know, archers didn't shoot to commands such as "draw, hold ...., loose!". Especially with high draw weight military bows, you don't want that "hold" in there.

Second, it appears that at least sometimes (and perhaps usually in large battles), archers started shooting at the same time, so that their first arrows were shot close together, but then shot independently.

Third, this movie trope is basically taking a system for muzzle-loading firearms in battle, and projecting it back onto earlier archery. For the guns of the time, volley firing was useful and effective. But the idea was not for all of the gunners to shoot at the same time - it was specifically for all of the gunners to not shoot at the same time. This was achieved by having 1/3 of the gunners shooting at once (or 1/4, or other fraction), and therefore 2/3 of them not shooting. With a 3 rank volley fire system, 1/3 of the gunners shoot, 1/3 are reloading, and 1/3 are ready to shoot.

Having that 1/3 ready to shoot matters! If everybody was to shoot at once, then nobody is ready to shoot for 20-30 seconds (at minimum). Enemy cavalry can cover a lot of ground in that 20-30 seconds of relative safety. This could be exploited. For example, in one case of aboriginal warfare in North America:

One of the Cheyenne chiefs called out to his people: "These people want to fight; now let us get ready and kill them." And Medicine Water answered, saying: "My son, Alights on the Cloud, will empty their guns."

Then, when everything was ready. Alights on the Cloud rode twice around the Delawares and close to them, and they all shot at him, emptying their guns as they tried to kill him, but the shots did not harm him. While they were shooting at him the brave Sioux on foot almost reached the end of the Delaware line. Now the Cheyennes all made a charge and the Delawares, having nothing in their guns, ran back and down into the ravine, where their horses were, but before they had time to load again the Cheyennes were upon them and killed them all. Some of them had the ramrods in their guns, the balls only half-way down the barrels.

as described in The Fighting Cheyennes (Grinnell, 1915); this tactic was often called "emptying their guns". Other examples are noted by Petersen (2016), such as Roman Nose attempting this against the US Army. (Crazy Horse's similar actions against Custer were more aimed to simply exhaust their limited ammunition, since faster-reloading rifles no longer allowed the time for a charge that had been available with muzzle-loaders.)

If, after a few volleys, the firing degenerates into independent firing at will, at least continuous firing is maintained. It is especially at the start of shooting that having soldiers ready to shoot (rather than having everybody reloading) is important. Despite this, guns were used for quite some time in Europe before sustained volley firing was adopted. This strongly suggests that archers didn't use volley fire in Europe. We can compare the Chinese case, where similar volley fire with crossbows had a long history, and the same method was adapted for guns. (See my comments in https://www.reddit.com/r/AskHistorians/comments/cktbv7/was_volley_firing_ever_adopted_or_possible_with/ (and also some early history of volley fire with guns in Europe and Japan).)

Everybody reloading at once isn't a real problem for archers - it takes much less time for archers to shoot again compared to gunners with muzzle-loaders. Where repeated volleys are shot by archers in movies, it's done for dramatic effect, not realism.

The question of archers shooting on command has been asked before, notably in https://www.reddit.com/r/AskHistorians/comments/7dqkbm/did_archers_really_nock_draw_and_loose_in_sync/ with an excellent discussion on advantages and disadvantages by u/Hergrim and u/hborrgg including guns as well as archery. Note that independent firing at will can lead to very hasty and ineffective shooting with guns; controlled volley fire will help control this.

References:

Grinnell, George Bird, The Fighting Cheyennes, Charles Scribner's Sons, 1915.

Tore T. Petersen, The Military Conquest of the Prairie, Sussex Academic Press, 2016