This seems to be several different questions so I'll take each one in turn.
Why didn't line infantry tactics try to keep up a constant volley of
I'm a little perplexed at the phrasing of the question because it implies that line infantry tactics did not "try to keep up a constant volley of fire". In fact linear infantry tactics were expressly developed to maximize the volume of fire (or conversely, as I'll briefly mention in a sec, to negate the advantage enjoyed by an enemy with a higher rate of fire). So, allowing for the basic reality that a constant stream of fire wouldn't become technically possible until the advent of repeating firearms, it is nonetheless the case that linear tactics did yield the closest thing to a "constant volley of fire" that 17th and 18th c. technology could achieve.
Often in movies on the American revolution and back when muskets were
common place the opposing armies would line up facing each other and
take turns firing. One side, then the other. Kind of like a volley.
While I'm not sure if this is historically accurate, brief research
online says yes.
Movies may be good at capturing the individual soldier's perspective of a battle--friends who are combat veterans have singled out "Black Hawk Down" and "Thirteen Hours" to me for particular praise in that department--but for a variety of reasons the tactical context of engagements tends to be set aside by the producers. Without dwelling on that latter point, suffice it to say the essence of infantry tactics in early Modern Europe resides in the details of something that the description somewhat glosses over: the "lining up facing each other" part.
Had cameramen been on-site to record the collision of Frederick's Guards battalions with the Austrian infantry at Leuthen (1757), it at times might indeed have looked like two sides "lining up facing each other": the two sides would draw close and exchange volleys. But the means mustn't be confused with the tactics: Frederick the Great and his opponent, Prince Charles, weren't simply lining their men up for a duel to let fate decide the matter; they sought what every general of the era sought: set the stage so that when both sides "lined up facing each other", their own side would come off the better. And so it was that early Modern European tactics emphatically did not center around lining up one's men and letting them take turns blasting away. Just the opposite, actually.
In some cases, generals might try to rush the enemy and put him to flight before his firepower could tell. The French and the Russians, whose infantry in the late 17th and early 18th c. was often inexpertly handled, were notorious for this. Oftentimes it worked, but other times, not so much. There was one funny episode where the notoriously lethal Dutch musketeers gave the French Guards such a proper thumping that Louis XIV, embarrassed, tried to ban French infantry from engaging face-to-face with their Dutch rivals unless they had overwhelming numerical superiority. In other cases, generals might make a demonstration to the enemy's front while using some element either man-made (cavalry, e.g.) or natural (a hill or a depression in the ground, e.g.) to conceal the movement of another force around the flank. Commanders such as Turenne, Marlborough and Frederick made their names by winning battles in this way. All European armies also made extensive use of light infantry, whose job it was to conduct reconnaissance, harass the main bodies of infantry, provoke premature attacks, pick off drummers and officers with their specialized rifles, and so on. Perhaps the best known light infantry belonged to Austria, which raised them from the regions of the empire bordering the Turks (themselves no slouches at this style of warfare).
To return to Leuthen. The movie cameras might capture the dramatic bits of the battle, showing men a few dozen paces apart blasting away with muskets. What they would not show would be the implementation of tactical maneuvers: The initial Prussian feint that led Prince Charles to over-commit his forces, including all his best troops, to the wrong wing. Frederick's lucky (and probably unintentional) use of an unseen Austrian blind spot in their view of the battlefield from the village of Leuthen. The impeccable timing of the Prussians' artillery and heavy horse, which both did murderous work on Austrian forces once these had been fixed or pushed back by the infantry. And so on.
So what did the Austrians in at Leuthen was the success of the Prussians in using the enemy's dispositions against him, not the superiority of the Prussians in a firefight (though, as it happens, the Prussians' more rigorous training often gave them the upper hand in those exchanges).
From a more tactical standpoint why didn't one army just shoot, then
have their first line duck and/or move behind the second line thus
allowing the first line to reload and the second line to shoot with
their already loaded weapons? In such a fashion that they would be
hot-swapping empty shooters with loaded shooters and not having any
quell in firing from their side. This always seemed like a point of
contention for me.
This seems like a question apart from the first two, to me. And a more straightforward one. (Here I'll borrow heavily from an answer I also wrote on QUora.) As the most popular answer to this question says, the concept described here was implemented in Modern times first by the Dutch, and it was actually inspired by the Romans. In a letter from 1594 to Maurice of Nassau, the prince's cousin William Louis goes into detailed discussion of a tract he read by the Greek military writer Aelian. In it, Aelian describes a Roman system for missileers--slingers, javelin-throwers, etc.--who were organized into six ranks. The first rank would release their weapons, then step back while the next rank released theirs, who would in their turn step back and make way for the third rank, and so on. The enemy would thus be subjected to a nearly continuous hail of missiles, with no single row of slingers or javelin-throwers becoming too exhausted to keep launching. William Louis goes on to suggest the adoption of similar practice in the struggle against the Spanish.
The Dutch adopted the new system with considerable success, and when the Swedes hired Dutchmen to train their armies in the early 1600's, they adopted it too, with similarly good results. Improvements were made along the way, but in broad strokes, for over a century, deep formations of musketeers were the norm. The drill called for musketeers to advance either by files, ranks, or divisions, shoot their weapons, then retire while the next firing group took their place. In other words, the paradigm laid out in the question, where some men fire, then are replaced in the firing line by another group, thereby maintaining the enemy under a continuous stream of fire, was the default. It's worth pondering, at this juncture, just how suited such a concept is to battle, that is, to a situation in which one might find oneself staring down an oncoming horde of enemy horse or infantry. And it's a question that makes the point: the predominant form of combat throughout the 17th c. and well into the middle of the 18thc., was not open battle at all, but a different species of engagement altogether: siege warfare, which isn't as cool-looking so isn't made into movies very often. Keeping up a steady tempo of fire by ranks or divisions in the presence of the enemy is challenging and dangerous, but rather less so behind entrenchments and chevaux-de-frise.
Eventually, a combination of political events and technological innovations brought about new systems of firepower deployment. Infantry formations became wider and shallower, and (counter-intuitively perhaps) volume of fire increased as a result. But this is actually an entirely different question--how the linear tactics of the 18th c. evolved from the pike & shot squares of the 16th and early 17th c.--so I'll leave that for another answer.
Arnold, Thomas. The Renaissance at War. London: HarperCollins, 2001.
Chandler, David. The Art of Warfare in the Age of Marlborough. New York: Sarpedon, 1994.
Childs, John. The Nine Years' War and the British Army, 1688-97 - The Operations in the Low Countries. Manchester: Manchester UP, 1991.
Duffy, Christopher. The Army of Frederick the Great, 2nd Ed. Chicago: The Emperor’s Press, 1996.
Szabo, Franz A. The Seven Years' War in Europe, 1756-1763. London: Routledge, 2008.