I mean there's you saying it's not effective then there's historical evidence showing they were really effective like for example the English longbowmen during the Battles of Agincourt, and Shrewsbury.
The Battle of Agincourt is commonly quoted by people in discussions like this, but without understanding of the full context.
The English longbows were strong, sure, but they were NOT strong enough to penetrate plate armor in anything but the most optimal circumstances (poorly-made armor with flaws in the metal, hit at the perfect range). Everyone discussing armor should have seen this by now:
So, the only practical way for a longbow to kill someone in full plate was trying to hit the gaps in their armor, e.g. groin, underarm, eyeslit. If they were on an unarmored horse, you could try to shoot their horse down.
And this is what the English did at Agincourt. The French men-at-arms were overconfident on the day, and made a disorganized charge up a very muddy slope into a well-defended English position which was guarded by stakes. The stakes and the mud managed to stop the cavalry from directly charging the archers, who could shoot down the French horses.
"Historian John Keegan argues that the longbows' main influence on the battle at this point was injuries to horses: armoured only on the head, many horses would have become dangerously out of control when struck in the back or flank from the high-elevation, long-range shots used as the charge started."
From this point on, Agincourt becomes an example
for the effectiveness of armor.
"The plate armour of the French men-at-arms allowed them to close the 1,000 yards or so (one football field) to the English lines while being under what the French monk of Saint Denis described as 'a terrifying hail of arrow shot'. A complete coat of plate was considered such good protection that shields were generally not used."
Enough French knights were still alive, despite the tactically moronic frontal charge, that they had to be killed by the English archers... using melee weapons; hatchets, swords, and mallets.
As for archery casualties at Shrewsbury, the answer is simply "most of the combatants were archers, and very few people were fully armored".
So full plate wasn't 100% invincible to arrows, but it definitely gave
very good protection, like 90%.
The armor used in Bannerlord's time period (lamellar, chain, scale, and coats-of-plates) wasn't
as good as plate, but then again, the bows used weren't as powerful as the English longbow either. Agincourt-era longbows could have draw weights of 150–160 pounds, while early medieval longbows (the best available) are estimated to be 80-90 pound draw weights.
http://myarmoury.com/feature_mail.html Padded, double-linked chain armor was considered basically arrow-proof.
Here's a youtuber testing crossbows against lamellar and plate. Both of them hold up quite well being shot at close range.
So, in conclusion: although it was not invincible, good armor gave high protection against bows and crossbows, even good quality bows and specialised arrows used by skilled archers. I think this is best represented in Bannerlord by T5 ranged infantry taking a minimum of 10 shots, on average, to kill T5-equivalent armor.
If arrows and crossbows were as useless as people are claiming, they wouldn't have been used at all in the Medieval Era.
Think about that statement from the other perspective. If arrows and bolts could be "really effective" against high-quality armor, as you claim, why would nobles bother to spend massive amounts of money getting it made for themselves? A bow or crossbow was far cheaper than a suit of good armor.
Bows and crossbows continued to be used, despite the very good protection a full suit of plate could provide, because
not everyone was wearing full plate (although by the late 1400s, a good 60% of combatants on the average battlefield were wearing partial plate) and so there were plenty of partially-armored or unarmored targets to shoot at.