archers did do a lot of damage at agincourt, they only fought with melee weapons after their arrows were all shot, which happened during the main push, which came after the knights were mostly defeated already. the main problem the knights at agincourt had was that not all plate armor was made of high quality armor, most of the plate armor used there was made of low quality metal.Agincourt was won because of difficult terrain, horses got stuck in, the arrows weren't the problem, but in the chaos the English archers killed off the knights with their cludgels. Also the Armour wasn't as fluted as a late 15th century armour is. It's the fluting or correct bending of Armour that makes the arrow not pierce through. So it should penetrate lamellar or brigandines without any problem for it is not as effective against arrows as a fluted Armour like a Gothic one.
it is true that well made plate armor, made of high quality metal is quite strong agains arrows. but not all plate plate armor was that well made, or of the highest quality metal. the well made armor of the highest quality cost a fortune, even most knights were not able to pay for it.