There are a number of ways to approach this question. The most obvious response is to say that, depending on how you qualify your meaning of "en masse," they did use the crossbow very widely. Crossbowmen were found in all western European armies, either to greater or lesser degrees. Kings and princes appointed royal officials as "master of the King's crossbows" and similar positions. They hired professional crossbowmen, stockpiled crossbows and bolts in their castles, invested in new crossbow technologies, and sometimes even participated in the rituals and contests of the urban crossbow guilds. A huge amount of time and money was poured into ensuring that crossbows were present in military arsenals and that there were soldiers trained in their use available for recruitment. Contrary to popular belief, there was no fear that the crossbow would upend the social order or concern over peasant crossbow use.

Another angle to this question would be breaking down the idea of what "en masse" means in a context of medieval warfare. Western European armies were generally smaller (ranging from the thousands to the tens of thousands) and were not standing forces. Armies were put together when necessary and amalgamated out of many smaller forces (the royal household, aristocratic retinues, troops drawn from garrisons, free companies of professional soldiers, foreign allies, militias, etc.) Raising an army was a fantastically expensive and risky proposition. A great deal of politicking and maneuvering was often necessary to generate support for the war to begin with, which might require political concessions or deals in order to raise the funds and support necessary to do anything. No one could be equipped "en masse" with anything because the organization, the supplies, and the funds did not exist in order to do so. Armories were maintained and stockpiled with armor, lances, ammunition, and many other types of gear, but these could not provide weaponry for everyone. Most often, soldiers were expected to arrive at the muster having equipped themselves, either at their own expense or that of their family/community/boss. No western medieval power possessed the money and bureaucracy to purchase 15,000 crossbows (plus additional strings, levers, and assorted bits and bobs of associated equipment) and distribute them to all of their soldiers.

Third, we should also consider the use of the crossbow from a tactical, battlefield perspective. If we were to somehow replace the equipment of all 12,000 soldiers in a theoretical medieval army, what would be the supposed gain of doing so? It is often a hard concept for modern thinkers to grasp, because we are conditioned to think of raw firepower as the end-all and be-all of combat. All too often, people get warped when looking at pre-modern weaponry and end up vastly overestimating the potential effects of missile weapons. A crossbow (or a longbow, for that matter) is not an assault rifle. It is not even a musket. The purpose of archery in pre-modern battles was not to outright slaughter the enemy purely through missile bombardment. That was simply not going to happen, even before the development of plate armor. Mail already did quite a good job of protecting its wearer from being shot to death with arrows. Even a padded gambeson can provide fairly good protection, especially at longer ranges. The main uses of missile weaponry were primarily to disrupt, delay, disorganize, and demoralize the enemy. If too many people have missile weaponry, then you're left without enough heavy infantry or mounted forces to take advantage of the disruption. Missile troops needed to be protected from the enemy, both with field fortifications and by their own heavier troops. Combined arms was always the order of the day on medieval battlefields and commanders were well aware of that.