Yes. There’s no doubt that the English longbows were a force to themselves. They were lethal in piercing armour but they were still used in generally the same manner. To open up the battle by forcing the enemy to take a defensive stance and “thinning the herd” (so to speak) before your own infantry engages their forces.

Once the infantry engaged however, you didn’t want to be raining down arrows on your own men and so the purpose of the archers largely changes to a completely different purpose; controlling the flow of battle with strategic use of volleys.

And yes…the Mongols changed everything with their horse archers. There’s a reason a good part of the population is descended from Genghis Khan…