I very much agree with your post in general, just wanted to nitpick a bit since I find the subject interesting
Padding was just there to stop the superficial scratches that arrows would leave when hitting mail.
Well... depends on what you mean by superficial I guess. While mail was pretty consistent in actually stopping an arrow it was not unheard of for a ring or two of the mail to give in and break from impact. This could give enough room for a particularly pointy arrowhead like the bodkin to give you a nice cut, not necessarily deadly but enough to impact your combat abilities.
Proper padding not only helped alleviate damage from partial penetrations but would actually make the rings of the mail less likely to break from impact due to its ability as a surface to give in and absorb force. For this reason the best (but also uncomfortably warm) padding was not leather or anything like it but layers of wool.
Padding had a similar role in melee combat. If a sword hits your mail it will not be able to cut you, but the sword is still a metal stick basically and being hit with it will hurt a lot unless you have something to help absorb that force.
As far as the penetrating power of arrows, only English longbowmen, with their heavy self longbows, could hope to penetrate plate armor, and even then, only at a moderately close range (around 100 yards)
I know the penetrating power of the longbow is a debated issue, but as far as I know the general consensus is that well made 1500s plate armor was pretty much impervious to arrow-penetration under any reasonable circumstance, even from longbows.
