If a 1400-1700 European army found its artillery crew dead during a battle, could other soldiers still fire the guns? Or is artillery-firing so difficult and arcane that only the most specialized troops can do it?
Firing a cannon is easy. The hard part of using cannons are reloading and hitting something.
Miss-firing a cannon is also easy, especially when done deliberately. Artillery batteries also tended to have rather large supplies of explosives close by, so any enemy unit that came close enough to an artillery battery to kill in melee would have ample options to make that battery completely useless for the reminder of the battle simply by destroying laffettes or an stuff the barrel with too much dirt and fire the cannon (the former would allow to recover the cannon, the later would make it completely useless) in short time.
Reloading requires a careful and disciplined crew in order to prevent miss-fires (for example remaining ember from the previous shot could ignite the blackpowder as it was stuffed if it was not carefully extinguished) and to achieve a reasonable rate of fire, so using an untrained crew would make cannons much less reliable.
The even harder part of using artillery is hitting your target at a reasonable distance, especially when aiming for troops. Against fortifications, one could still use the try-and-error method and adjust the aim until the target is hit, but since troops would move, that method is virtually useless in field battles. Predicting the trajectory of a cannon ball with an non-neglectable arc, secondary physical effects like the wind or the magnus-effect and potential "features" of the cannon (slight imperfections in the barrel) or ammo (not perfectly spherical) required apparently such an extensive understanding of mathematics that the best schools in France was dedicated under Napoleon to the education of artillery officiers, the famous ecole polytechnics. Of course such well trained officer were never available in sufficient numbers and generals had to make due with whoever they could get - at cost of a reduced performance of their artillery of course.