That is what I meant with economic benefits (by the way, it wasnt so much about training someone to use a bow but about finding people who are strong enough to use 100lb draw strength bows over a longer time.).
Sure. And, equally importantly might be the amount of time required to train someone to minimal effectiveness. Despite the utility of the weapon, no nations outside of England and Wales made much use of the longbow. The problem was that to reach a minimal level of competency required regular practice with the weapon for years. Whereas, minimal level of competency in a musket could be achieved in two to three weeks. If you are trying to train up an army, that's a big difference in cost.
But what RPG actually models this things?
Most RPGs don't model or don't spend much time modeling the PC's as lords over domains. In 1e AD&D I wrote up about 20 pages of house rules regarding training militias up to different levels of fighting quality as fuel for a domain/prince driven campaign where figuring out what sort of militia a ruler could levy had real meaning. But most games don't go into that in detail. Birthright arguably was headed that direction, but it never gave really good examples of play. Pazio published a 'Campaign Guide' that had some really good ideas on domain management, but it didn't go very far on that. The big problem is that there just isn't much demand.
Most of the time there is no strength requirement for bows.
That's debatable. It's potentially much more effective to have high strength in D&D, and its certainly much more effective to have at least average strength.
Fatigue is hardly modeled at all (constantly drawing a bow tires you a lot more than filling in gunpowder)...
Fatigue is often ignored, but partly because battlefield scale engagements are generally not the focus of play. D&D normally has combats that last only a few seconds, not hours. A combat that goes 10-15 rounds (60-90 seconds in 3e) is a long combat in D&D, but isn't even as long as a boxing round. To a certain extent, that's realistic for the sort of very small scale engagements D&D has.
So in RPGs there is usually no reason at all to use guns, especially the very early ones or ones with the historical disadvantages (missfire, long loading time, etc.)
In RPGs there is usually no reason at all
for PCs to use guns. And that might even be historically realistic to the period. Highly trained individuals in the period still generally relied on skill with melee weapons, perhaps after discharging a pistol or two at fairly close range. The biggest advantages from firearms are generally going to be observed in low skill combatants - not high skill ones. Consider the historically accurate attitudes (if not the actual effectiveness thereof) toward the firearm captured in Kirosawa's 'Seven Samurai'. Here the musket is represented as a quasi-magical device of seemingly infinite range that can reach out and cause instant death in even the greatest warrior. What is important about that is not so much whether that is a realistic representation of early firearms (it's not), but that it captures perfectly the revulsion the samurai caste had to the appearance of firearms. They were just so 'unfair'.
As it is wryly said, "God made men. Sam Colt made men equal."
So what use is there in having "historically accurate" early firearms when all their disadvantages are represented in the game but their advantages are not?
Properly modeling historically accurate early firearms makes them useful for low skill individuals. One way to capture that correctly is to make them 'simple' weapons even commoners are proficient in, rather than the 'exotic' weapons they are usually presented as. One of the reasons I've never brought firearms into my game is that I know that NPC's will benefit from them vastly more than the PCs can.
The key thing to observe is that the periods of history that correspond to periods of classic heroic myth tend to correspond to eras in which defense greatly outclassed offense. Homer's Illiad & Oddysey recounts the era when early bronze heavy armor and weapons first appeared, rendering those warriors so equipped nearly invulnerable to the light weight skirmish weapons the majority of foes were armed with. During this period, one well trained individual equipped with the latest high tech weaponry really could stand against 30 conscripts with obsolete weapons. Likewise, the age of chivalry recounts the period where highly trained soldiers on horseback and clad in high tech steel armor could defeat any dozen conscripted unarmored infantry in a pitch fight.
The firearm doesn't completely negate armor, but it does partially negate armor - rendering one of the most expensive advantages an aristocrat could purchase partially or completely ineffective. Early firearms don't allow a single person to take on great numbers of foes simultaneously, but it does allow great numbers of foes to take down a single skilled opponent. In other words, the firearm is a conscript's weapon - easy to use, requires no great athletic ability in the traditional sense, effective in mass, effective at range, and defeats all but the most expensive counter-measures (and even those some of the time).