Strength as a firearm damage modifier

Strength is commonly used as a damage modifier with melee weapons, but what about firearms or crossbows for that matter (specially the heavy medieval ones). Should STR increase damage by such weapons and why?

Crossbows store their energy in a metal bow (also called limb, lath or prod). In the heavier models this is pulled by a set of pulleys in such a way that the crossbow can store more energy than what a normal human can pull. This makes it seem  like the amount of energy in the bow (and thus the bolt) can be independent of the crossbowman's strength. The same reasoning goes into guns. After all gunpowder isn't going to burn faster or brighter because one's character is stronger.

So why should strength relate to damage? My reasoning behind this is weapon weight and momentum. The bigger the bow the heavier it is. The bigger the bullet, the bigger the gun and also the recoil associated with firing the gun. As I mentioned previously in this article (Aiming, what is it and what's its worth?), aim is strongly related to damage. A sure shot is more damaging that a flesh would and certainly more so than a miss. The stronger the character the firmer the aim and the surer the shot. The stronger the character the better recoil will be handled (an issue with magically reloading crossbows too).

Something also goes on with small weapons. Being humans are not hydraulic and all, high strength is usually associated with a bigger body. A small weapon may simply be too small for the character's hand. Too much strength and too small a gun may be actually counterproductive. There's a sweet spot after which added strength becomes counter-productive.

So it isn't about having the maximum possible amount of strength, but rather having the right strength for the weapon at hand. This is something we may lose sight of in escalating-hit-point games in which the first round of combat most surely will not be the last. But when the first round may be the only round of combat making sure your character hits first and hits well is of vital importance. Having the right strength becomes more important than having the best strength. Take a moment to think how this relates to character building as well as gender and racial differences. It seems my halfling no longer requires the Desert Eagle to be effective in battle! Thank goodness, those bullets were costing me a small fortune.