Longbows could not put an arrow through plate armor except at extremely close range. This doesn't mean that men wearing plate armor were invulnerable, though. An arrow could still find a chink or a gap in the plate where mail covered a joint and cause a wound. Even more significantly, a knight might be able to wade through arrow volleys, but his horse would not be as fortunate.

That aside, the main reason for the mass use of the longbow in the late medieval English military isn't really because of the attributes of the weapon itself. That's not to say that a longbow isn't a dangerous weapon in skilled hands (because it absolutely is), but to compare statistics on range and rate of fire with other types of bow or crossbows is missing the point. The effectiveness of the longbow in combat depended on having a large number of archers delivering volley after volley into enemy ranks. The need to have that many archers available for military service was recognized as a vital necessity by English kings, who passed numerous laws and statutes legally mandating both ownership of and practice with longbows. A municipality which did not maintain proper archery butts or practice fields for archers to use could be fined. A man found to not own a bow or skipping practice could also be fined.

People were also motivated to practice archery because of the potential financial rewards of military service. In the early 1300s, English armies transitioned from a levy structure to a paid contract structure. Standard pay for a foot archer in the new system was generally above wages for skilled labor (like carpentry). That pay was in addition to the possibility of loot acquired on the campaign. Some of that loot would be handed over to your captain/the king, but on the whole, the system was pretty fair. In fact, serving as an archer was so financially lucrative that many longbowmen continued to serve as mercenaries for other European monarchs and powers after their "official" service to the English crown was over.

Anyways, the broader point is, there was a large pool of men in England who were trained with longbows. They were motivated both by the punishment levied for not doing so and also for the possibility of significant financial benefits from service as an archer. This large population of archers, combined with the new contract structure, allowed English kings to quickly call up thousands of men for campaigns in France during the Hundred Years War. These structural reasons were what created the large longbow units that carried the day at Crecy, Agincourt, and so many other battles, rather than the inherent advantage of the longbow as a weapon. The English certainly utilized the longbow's attributes to their fullest extent, but it in itself was not a "wonder weapon" or particularly innovative technology.