Yeah I know what you mean. But I think at the same time, giving them piercing damage makes sense. The steel-tipped pointy arrows like bodkin tips, and a lot of the arrows we see in the game for that matter, were designed to puncture armor. In fact, the tip would leave often smaller wounds that a hardened warrior was likely to survive if it missed vital organs (kinda like bullet wounds from modern times) unless the wound got infected. But it will at least stop an armored knight, and that was the point, pun intended.
The big damage arrows were the barbed, flat/broad head arrows, etc., which did a poor job of penetrating armor but left such big wounds that trying to pull them out would often cause more damage to tissue. A battlefield surgeon was often called after the battle to pull out the wound properly, but it seemed like many troops would not survive a chest hit from one of these damaging weapons.
And yeah it's sad that we can't make it so that the damage type is connected to the arrow instead of the bow.
In real life, I would imagine there to be a huge difference between a bow with a light draw weight and a bow with a heavy one. You can ask anybody that practices any form of archery (not that I do, but I've been observing it). I've seen videos of people pulling those 100 lbf bows. It's not the toughest bow, and is lighter than the average war bow, but it looks really powerful. You can see the arrow's flight and impact. If it were tipped with bodkin or something, it can totally punch through an iron plate.
If you're lower tier troop, a young man that's only used to lightweight bows that you use to shoot rabbits and deer in the woods a few times a week to feed your village, suddenly recruited from your village and thrust into a military life with barely enough training because of the urgency of war, I think it's completely viable to think that their officers would set them up with bows that they know they can use, and train them in using heavier bows along the way. In the game, this translates into upgrading to a higher tier, which allows them to use a heavier bow.
Bottom line is that there should be a difference in effectiveness between low tier and high tier archers. In my opinion, the difference should be big, but it should also be that similar-tier troops can kill each other in one or two shots if they actually hit, which is certainly the case.
Besides, in reality, my tweaks have made it so that tier 2 archers can actually damage an unarmored opponent. I tested this by wearing light armors (total body armor of 24) and only two shots were enough to kill me without a headshot (headshot is fatal on the first shot).