longbows had nothing to do with english success at agincourt, archers were just dirt cheap compared to knights so they hired a bunch, any arrow would fuck up unarmored horses (which is all they accomplished with ranged)
tho humorously I believe it was Agincourt where italian crossbow mercs tried to do a few volleys, but because of rain they had wet strings and couldn't shoot so they got scared off by the english archers. the french knights then immediately cav charged their own italian mercs for being cowardly ranged, and killed most of them themselves
Perhaps not the direct reason for victory, but to say their unrivaled range on that battlefield and their hitting power had no effect on the outcome is ignorant. Sure, it could have been another European Bow or a Crossbow or something, but the former didn't hit as hard and the latter had a far slower rate of fire. Plus those "hired archers" you speak of, they come hand in hand with those Longbows, they probably spent hundreds of hours practicing with their Longbow. Sure, other bows and crossbows could have wounded and killed those Horses, but the Longbow would have done it better.
It was the Battle of Crecy where the stupid French killed the Genoese Crossbowmen that retreated from the English arrows. The English had unstrung their bows and kept the strings dry during the rain before the battle whilst the Genoese couldn't do that with their Crossbows without tools.
But yeah anyway on topic, INB4 Katana better than European swords.