There are plenty of reasons why people would break formation and seek out individual combat. premodern / barbaric / blabla doesn't figure into it. When you break formation and seek out individual combat right in everyone else's view, it's a grandiose opportunity to gain prestige and status
I don't think this is true. When you break formation in front of everyone against orders, you end up getting in
very deep trouble with whoever happens to be in charge.
Spanish tercios had severe punishments for breaking formation so they could "prove themselves", because that was
not tolerated in a disciplined force. You will note that Tercios also seeked out distinction (not loot) by breaking formation, but they never had shields.
When you do it in the middle of a battle, seizing an initiative to seek out an enemy in the middle of a meelee, hacking him down all by yourself gives you the right to claim all his stuff as loot and may make you a rich man instantly.
[Citation Needed]
I don't think war profiteering works on a dibs calling system. I sure wouldn't like to be trying to pull platemail off of a corpse in the heat of battle so that another noble didn't take it first.
(Read the Iliad, Homer has the warriors all eager to hack each other down and claim booty, and he even describes how many victors only enjoy their loot for a few brief moments before the next man, in turn, hacks them down.)
Most historians who study Ancient Greece preface the Iliad with "ABSOLUTELY NONE OF THIS EVER, EVER HAPPENED". More importantly, the Iliad is an idealisation of combat by authors who had never actually seen it, rather than a legitimate source of what combat is actually like.
You don't earn much in the way of loot if you always stick with your formation. But the armor/weapons/horses of your enemy are often enormously expensive pieces of equipment. Why leave it to the cavalry, or the officers, to rush in and claim all the stuff?
Because that's not how looting actually works, you get loot from whoever happened to be living in the village next door to the battlefield, not in the thick of battle.
There may be rational reasons why you would, in some situations, have armies full of warriors who look forward to single combat, and who go to lengths to acquire gear (like a shield) that lets them face those fights with confidence. In other situations, soldiers might not look forward to it all that much because there'd be much risk and little to gain, so they are going to stick to their buddies and not go out seeking high risk situations. What previous posters wrote about Japanese and Chinese peasant armies makes me consider it likely that most troopers would fall in the latter category. Hence supporting the theory that there are social reasons why shields weren't used so much in those cultures even before gunpowder became prominent.
I'm still skeptical that it was some sort of lust for gold and blood within the semi-nobility that made them use shields for one-on-one fights to the death, while the cowardly and meek peasantry used two handed weapons because they weren't alpha enough to break formation and steal someone's gold plated codpiece.
It's not so clear cut as that. The Normans at Hastings did not ride down Harald Godwinsson's shield wall - they fell on the Saxons and won the battle after the Saxons broke formation and pursued a bunch of fleeing Normans. Why, pray tell, would they have broken formation, if holding formation was so super great on their minds, as you claim? Holding formation is what's unnatural to a warrior. Throwing yourself on the enemy and hacking him down, that's what all your instincts push you to do, when your blood is up, and when you sense that he is weaker than you.
Because the Saxons that broke formation thought the Normans were fleeing and thought they could chase them off the field, which was a tactical decision - not because their murderboners overwhelmed them to the point of needed to crush the Normans in honourable combat no matter what.
Homer's Iliad was a hugely popular epic throughout classical Greek and Roman times. They wouldn't have kept on retelling that story if the whole "glorious individual combat" thing of Homer had been an alien concept to those Greeks and Romans.
As I said, the Iliad is as much a realistic depiction of ancient warfare as a Tom Clancy game is to modern warfare.
EDIT:
On reflection, I feel that while you're right to a certain extent about the shield being used for self defence by swordsmen/axemen who lack the range of polearms, the reasons
why you think that are really, really wrong. So to reiterate, it's not that shields aren't good for the rare one-on-one fight with an enemy, or that people didn't occasionally get taken by the thrill of battle, but that the shield's use as a tool in warfare wasn't completely and totally shaped by these factors.
More importantly, in Japan (which is the focus of the thread), shields never really caught on. And we all know how much the Japanese loved to duel one-on-one because they wrote down their favourite ones in historical documents - so how come shields weren't an integral part of warfare here?