They actually did, I seriously do not understand why is it so troubling to understand that everyone had nobles who could afford armor, even the Tatars and the Turks.
It is really not a difficult concept to figure out.
The average 12th/13th century Tatar/Turkic noble wore more armor than an average European noble, especially if we consider their horse barding.
You should not abandon video evidence, but should rather just be critical of them.
Of course there are videos of armors being penetrated, but those videos always show some LARP festival tinfoil instead of properly hammered and forged armor.
What you can do however, is accept video testing done by actual historians with degrees and test done in controlled environment, like these ones;
Testing of longbow bodkin point, simulating 140 lb warbow fired at point blank(few meters) range;
https://www.youtube.com/watch?v=D3997HZuWjk
Testing done by the British Royal Armories to test the deflective capability of curved plates;
https://www.youtube.com/watch?v=E8FGmqU25JQ
Basically, all videos and tests that show that armor works are those done properly.
There is a very good reason why people spent mountains of gold on armor.
Yes it does, and every single one of those goes in favor of the armor, for armor works the same in all situations, while the performance of bows can be weakened by everything you just mentioned.
Which again goes in favor for the armor, because modern tests are done with both armor and arrowhead being of the same quality of metal, while historically armors were usually made of higher quality steel and were hammer hardened and often forge/process hardened while the vast majority of arrowhead findings that we have are low processed low grade wrought iron.