The game's pretty much spot on. Most of the complaints in regards to how "bows are OP" in the game, usually come from opinions that straight-up
refuse to take into account the discrepancies between real-life conditions and in-game conditions.
For example, most "bows OP" commentators...
- ... base the argument upon personal anecdotes devoid of actual information, and rarely give accurate account of what the combat situation was -- most importantly, they very often conveniently omit the information about the combat distance, and the action they were performing when they were shot.
- ... usually just ignore the fact that in-game, both the likelihood of arrows actually hitting you and doing any real damage (when properly armored) is pretty low at long distances.
- ... usually do not tell you that they were shot at (1) under 50 distance, (2) as they were closing in to charge, or (3) were just on their way out from a charge, (4) against MULTIPLE archers targeting the person. This has come up repeatedly, and to my knowledge, no "bows OP" opinion ever really addressed this. It's simply ignored.
I've brought it up before, but studies on the Japan's gunchujyou(軍忠状) have shown on average around 60% of casualties in Japan's medieval warfare were from ranged weapons, with both early and late Warring States Period showing arrows as the No.1 reason behind casualties. A "gunchujyou" is an AAR of sorts where lords that have participated in combat submit to their overlords, which record down their kills, deaths, and reasons behind deaths (in order to compensate, reward, or memorialize).
While it is difficult to compare directly, still, medieval Japanese warfare, and social conditions were the most comparable to Western medieval warfare in terms of social formation, structure, armament, and scale and voracity of warfare -- whereas Chinese warfare, for example, would be much more difficult to compare directly.
So unless there is something incredulously different between Japan and the West when it comes to shooting bows and getting hit by them, it would be safe to assume the efficiency of bows in combat were largely comparable between the two.
The reason why bows are sometimes deemed OP in the game, is very simply because player armies recruit and train high-tier archers way faster, in way larger numbers, way more easily than AI armies. Typically, AI armies do not build up a strong band of archers in any meaningful numbers, which means at initial phase of battle
the AI armies don't have a "skirmish phase" where archers from both armies exchange fire in hopes to do as much damage to the other, as possible.
So, from the initial phase of battle the player army with significant number of archers can simply dish out one-sided punishment to the enemy armies, dealing huge losses in numbers as well as overall morale, even before the main melee starts. If the AI armies had a tendency to balance out their own armies with quite the number of archers, and they would send their own archers to counter the player archers every time, then the archers won't feel so OP anymore.