Firing bullets in volleys became a standard in part due to the tactics of Gustavus Adolphus, 'father of modern warfare' and King of Sweden during the Thirty Years War from 1618-1648.
Now, what Gustav brought to the field were a number of new tactics and new applications of old playing pieces. In particular, with muskets. Instead of having everyone formed into massive pike squares, Gustav went for a combined arms approach, in particular with musketeers and cavalry working together. In order to break apart the large pike formations of his day, Gustav would have the musketeers shoot a massed volley into one part of their ranks, and then charge the cavalry through the hole that had appeared as a result. This was, apparently, devastating and when combined with other innovations like his reformed artillery was very successful.
TL;DR Firing at will would certainly have got more shots out in a minute, but that was never the point. Volleys allowed those shots to take maximum effect and actually weaken the enemy.
Source: http://www.amazon.com/Gustavus-Adolphus-Profiles-Michael-Roberts/dp/0582090016
The rest of this post is speculation. Given this, it is plausible to suggest that in other situations volleys were equally useful for creating morale shock. It may be the case that killing ten men at once has a greater effect than killing 15 men over a similar time period. One might suggest the sudden drop of bodies would impede a charge, or terrify the rest charging: alternatively, you could argue that from the perspective of the shooter a volley keeps one focused on the task at hand. I'm not overly convinced by arguments based on that but it's plausible.
It's also worth noting finally that certain firing drills with muskets practically require firing in volleys: if you want to fire by rank, for example, with first, second, and third ranks of people all firing then you need the first rank to fire all at once so they can then get out of the way of the second rank, and so on and so forth. That situation certainly makes volley fire produce more shots per minute because it allows more soldiers to shoot. Likewise, something like 'platoon firing' (volleys in groups travelling along the line rather than down the ranks) also require a degree of synchronisation.
One advantage I can think of is that it keeps people firing like clockwork, if you let the men fire at will some will spend to much time picking a shot and worse, thinking about what they are doing which is not a musketmans job. For much more info check here
Arrows and musketfire was not very accurate over larger distances, instead you went for the spray and pray approach. Arrows, especially when used by English and Welsh Longbowmen were fired at a ridiculous pace, up to 6 a minute, although it was possible to do more. That's 6 waves of arrows a minute. I'm on mobile so can't find the source right now but I think I remember a source saying the sky was blacked out with arrows,there were that many there.
Basically when there's that many then you can't dodge them, and the continuous assault would kill many, as the English certainly proved in battles such as Poitiers, Crecy and Agincourt