As you've been discussing, many historians say the English arrows wouldn't have been all that effective against plate armor at Agincourt. Studies seem to confirm that longbows of that draw weight, though damaging, wouldn't have slaughtered the French knights. History confirms this, noting that the French knights rode all the way into the lines of English archers, which is why the English archers yanked the charging knights off their horses after the horses ran into the forest of English anti-cavalry stakes. The few period accounts also say that once the French infantry was in contact with the English infantry, the archers swung the tide of battle by wading in with hatchets, stakes, swords, and clubs.
It's simple to note that if the arrows were having tremendous effect, the French infantry wouldn't have been able to slog through the mud all the way to the English line, arriving in such numbers that they badly outnumbered the English (as the theories about the crowd dynamics and funnel effect indicate), nor would the archers have necessarily stopped shooting and opted for hand-to-hand if their arrows were swinging the tide, except maybe to avoid hitting the English infantry in the side of the head.
Here's a link to the crowd dynamics theory of Agincourt.
crowd dynamics link It's based on studies of crowd disasters at rock concerts, and I have profound doubts about it. Infantry that mashes together into a clump or wad on an open field before meeting the enemy is just too dumb to function as infantry. A high-school marching band wouldn't even do that, much less trained and disciplined soldiers following the orders of trained and experienced commanders, and by all accounts the French commanders had proved both able and experienced in previous battles. My other problem with the crowd theory is the fact that any lopsided kill ratio due to an overabundance of front line soldiers should be eliminated when that overabundance gets thinned out.
My pet working theory is that the English dug their archers in as tactical necessity - combined with brilliant deception. Continental archers always fled when stripped of infantry protection, and when the massively outnumbered English line broke, the French would expect the rest of the English formation to collapse, the archers running for the hills. The French waded up to the English line of 500 men at arms, not realizing the two wings of 6000 archers also doubled as a pair of Scottish schiltrons (essentially pike phalanxes), and were enveloped from both flanks by soldiers who had a tremendous reach advantage with overlapping pole arms. If that's what happened, it doesn't require the French to be idiots, nor the English to be idiots for fighting against such overwhelming numbers, even goading the French into precipitious battle. In fact, it predicts that the English would want to goad the French into battle before the French commander started pondering the massive wings of English archers standing in a forest of really long pointy things. The muddier the field, the longer it would take a sword equiped infantryman to traverse the length of a spear or pike, and the more lopsided the kill ratio would become.
In sum, I think it's more likely that Henry used brilliant deception to lure the French into battle on poor terrain offering limited maneuverability, just like William Wallace at Stirling or Robert the Bruce at Bannockburn. Then he goaded them into attacking without pondering, just like William Wallace at Stirling or Robert the Bruce at Bannockburn, before they became worried about the vast number of archers as forming some sort of infantry. Then he enveloped the French lines from both flanks with his pole arm formations, holding the middle and pushing in from both sides to form a kill box, using schiltrons like William Wallace at Falkirk or Robert the Bruce at Bannockburn. To Henry V these tactics should've been as natural as breathing, the stuff of legends round the campfire, and he accomplished a maneuver that his tacticians surely dreamed of. In this view both commanders and their armies are highly competent, but the English had a depth of experience, an innovation adopted from Scotland, and a brilliant tactical deception up their sleave, thus carrying the day. I prefer it to the idiot Olympics that the crowd density theory implies
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