Yes, from a munchkin perspective, or from a "most effective unit type not considering how it comes into existence" perspective, lifelong-trained English longbows probably are a more effective unit type than typical musket infantry. "Lieutenant-Colonel Lee of the 44th Foot" had a good point. The rate of fire and accuracy was generally far superior.
From the perspective of what it takes to "get" lifelong-trained English longbows in one's army, though, it's not just a button the king clicks in Sid Meier's Civilization.
Those troops were exceptional, with specialized powerful bows, lifelong training including great skill and strength, bodkin arrowheads designed to pierce armor, etc. At Agincourt the battle conditions and French tactics from overconfidence were also large factors. It's interesting too that the English were almost as surprised as the French that these troops could defeat heavy cavalry. (Relevant to the "do you like to know the game values?" question. The French player probably got upset.
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Less spectacular archers in other circumstances were not so great against armor. Shields are also fairly effective countermeasures to arrows. Even if an arrow goes through a shield, a shield penetration won't be killing the target.
Most archers though were specialists, even back through ancient times. Bows are not as easy to become competent with, as guns or crossbows are. Training time is important to the overall cost and difficulty of fielding a troop type. Also, most people in a society, government, and even the military, are neither munchkin-minded nor do they understand tactical issues very well. Most people think "gun > bow". After all, look at the fire and smoke.
PvK