Yeah right, because whatever you can steal from villagers (food? clothes? a few animals? some coin?) is so much more valuable than that slain warrior's equipment, for which he paid the equivalent of a several year's wages, and which is now just lieing there on the battlefield for anyone to grab.
Armor and weapons are also, like, 100x better portable than the cattle or goats you might get at the village. They are the best thing you could loot, aside from a coin hoard. Why would those things NOT be the #1 loot (okay, #2, after coin and jewelry) to bring home from a war?
Is this actually based on historical fact or is this just another thing you're assuming based on your giant misconceptions of logistics and warfare? War isn't a MMO. You can't just "pick up" someone's armour and weapons immediately in the middle of a battle once you've killed them, not even if you've killed them in this fabled single combat thing you seem to think totally war is based around.
You said it yourself, coin and jewellery was worth a lot more. Where would you get those things? Stealing from settlements over the course of a whole campaign. If you're Roman or Viking, you could take some towns as slaves too; under the Marian Reforms legionaries were practically paid in slaves, which were worth far, far more than a dead gaul's moustache-guard.
And even without that considered, it still doesn't even remotely make sense that the entirety of warfare and tactics is shaped by people wanting to ragekill the enemy and steal their socks.
Also, ignoring everything else that's everyone's said and only replying to one point doesn't make you somehow less wrong, you know.
But what do you do with other arm instead? from what I can tell:
a. you can use it, along with the other arm, to hold a two handed weapon. This offers even less protection compared to a shield, especially against projectiles.
b. you can wield a parrying dagger, which is better defensively, but still not as a good as a shield.
To me, these two options don't seem to prolong combat survivability compared to a shield.
Also a shield can be use it offensively, during a charge for example and to bash an opponent away during one-on-one combat.
Well, from what I read, two handing a really, really long spear was a good defence against a cavalry charge because it keeps them as far away from you as possible, and was good at attacking as you could poke the enemy from far away without the being able to retaliate if they didn't have a similarly long polearm. It didn't protect them from arrows, but by that point Japanese strategy had tended towards cavalry and away from archers (
which apparently we have the mongols to thank for).
That being said, sometimes the norms of combat aren't always the most efficient possible equipment and strategy used in the best possible way in that context - it could be that not using a shield was prevalent in Japan simply because it had become an unquestioned norm of combat.