A lot of these arguments make a few common mistakes (often both sides of the argument). For example:
Just because powerful bows aimed well could penetrate heavy armor doesn't mean that you could rely on them to consistently do so.
Similarly, just because you could March around in plate impervious to many standard attacks doesn't mean you weren't vulnerable to being ganged up on, slow, and in trouble if you got knocked over.
Nearly always people like to compare best case scenarios of one side to worst of the other, or someone who is very competent or lucky to someone who is not.
It's like when people compare martial styles: They often wind up with a scenario where they show one side (the one that they prefer, or know more about) doing their shtick well, and the other side doing theirs poorly.
The truth is, it often comes down to exceptional people who have had good teachers, are well-equiped, understand what they are doing, make the right decisions at the right moments, and get lucky do very well against those that fail at one or more of the above.
And you can't maintain all of the above for your whole career, either. Age and ego play a factor, too.
I would also note that for the most part D&D combat doesn't resemble armies at war, it models small skirmishes. Most characters are not going to be the target of dozens of arrows flying their way in a volley. Throw in that the quality of armor varied widely from crudely made and was better than padded to the highest quality steel custom made for a wealthy individual along with technological advances that varied from region to region.
But my point from earlier still stands - if that incredibly expensive armor wasn't effective most of the time it wouldn't have been used.