No you are right - Chain Mail is better at defecting arrows due to the force being distributed over a larger area. Plate mail does not have any give, and it is not that thick so arrows quite commonly would puncture through plate mail.
Plate is good against blunt and sharp weapons - but wieght hampers your fighting style - really no advantage or disadvantge for either.
Chainmail is pathetic against Arrows tho, unless worn with a material that forces the force across the chainmail, like leather, chainmail itself doesn't do all that much, it is combination of chain-mail and another material... usually leather. Then again, other then shields, what other protection is there really against arrows... that said, arrows are better at wounding then killing in reality. It's a lot harder to kill somebody with an arrow then a sword. Since arrows would realistically need to kill and yet players not be killed too quickly by them, I don't think the idea of certain armors are weaker to certain attacks is overall a good idea for gameplay balance reasons, just like I think arrows should do more then just wound a creature so that it'll eventually die... after it's digested your sorry butt.
All this said, I wouldn't mind seeing Resist Normal Weapons and Magic disappear and instead armor gaining secondary stats of Archery defense, Weapon Defense, Magic Defense and Unarmed Defense what vary between every single piece of armor but carry a bias based on the armor material, with vendors always supplying armor that is balanced in all categories but at later levels then you can loot it. So that you can if you want, figure out what enemy are weak to on a more individual level, after all, not all plate is identical and not all chain mail is identical, not even all leather is identical either. Maybe... possibly also a spell that shows you the relative defenses.