The longbow wasn't exactly able to "pierce armor," especially at longer ranges. While it possible for a longbow volley to cause casualties at every possible range, the sources are pretty clear that longbow arrows did not kill by outright punching through plate armor, but by striking less-protected gaps in the armor, hitting men who had their visors raised, or killing/crippling horses (potentially causing the rider to be injured). The purpose of longbow archery is to disrupt enemy formations and hinder their ability to fight as a unit. This requires large numbers or archers, which brings us to your second point: how the longbow impacted warfare.

The longbow itself was not the basis of any kind of military revolution. What changed English warfare and allowed for the famous battlefield victories of the Hundred Years War was the gradual development of armies entirely based on contracts of service, which created forces that were quicker to mobilize, better equipped, and better organized than previous recruitment structures. English kings (assuming they had the political support/stability to go to war) could rapidly raise relatively large numbers of troops, many of whom were either professionals or at least semi-professionalized. Many of these soldiers would be longbow archers. It is absolutely vital to understanding English longbow archers in warfare to know that the archers were 1) often mounted, allowing for rapid movement on campaign and 2) actively took part in hand-to-hand combat after the enemy had gotten too close. The longbow was only a part of what made the men who carried them so valuable on the battlefield.