Further, since we are digging into this, almost every unit has both layers of armor and at least some form of armor. Most archers simply do not have the ability to get to enough power from range to kill at significant distance.
For example, roughly speaking a bow with a draw weight of about 100 pounds will probably hit at about 120 joules max, at a decent range of, being generous, 50 meters. Energy dropoff is significant every little bit of range we add, and reminder we are being generous with that distance.
Warbows range from about 100 to as high as 170 for the most part in the medieval era, but bows are rarely consistent across a unit of archers and generally speaking you want your entire volley to hit with full power so you probably aren't planning your shooting around the one or two foresters you conscripted who can shoot a nice 160 bow at full strength.
120 joules is enough to kill someone in a gambeson or iron plate with relative consistency, and barely scrapes enough to kill someone in both.
It is not enough to kill someone with steel plate and only in rare circumstance enough to penetrate. It is not even close to penetrating or killing someone in steel plate with cloth padding underneath.
Another complicating factor is that the arrowhead affects the force of the impact as well. Maybe professional archers will have nice bodkins, but the majority of your squad is probably conscripts with shitty homemade heads or non-bodkins and this further reduces your penetrating power.
Fatigue is also a factor. We are assuming firing at full strength here, and it's extremely likely that most archers do not shoot at tip top shape after a few volleys. They might only be able to quarter or half draw the bow, further reducing the effectiveness of the shot. After all, with a 100 pound bow we are asking them to repeatedly pull that force, aim, shoot and handle recoil, then do so again under stressful conditions (someone is charging at you).