It's the disadvantage of recreating historical martial arts in a realistic way; if you actually did it completely realistic, you need to figure out what to do with all the bodies.

That can't be completely true - historical soldiers still needed to train. So, in theory, we can still recreate their training with historical accuracy. And I imagine their training still had the concept of winners and losers, even though both people walked away to train another day. I imagine their training would look a lot like the sport fighting in the linked video.

Yes, they trained, but their training wasn't realistic combat. They used blunt, often wooden swords, for example, or practiced stuff in slow motion. And we do the same, but it's not the same as actual combat, because in actual combat, people get hurt. You can get a perfect simulation of that without people getting hurt.

In Germany around the 16th century, people fought unarmored with blunted swords, and the winner was the first guy to cause a bleeding wound on his opponent's scalp.

We certainly could reproduce that today, but I don't think most people would want to. :)

Swiss pikemen and (briefly) spanish swordsmen aside, foot soldiers were either horse or archer fodder.

The implicit contract for military support between the King and the areas he ruled changed in the Dark Ages: instead of providing many men, you provided few mounted men (a requirement that led directly to the feudal system).

So many other people here are correct in pointing out that these sword skills weren't the most relevant thing to the conducting of all-out war.

Nonetheless, europe was pretty martial, and there were a lot of martial contexts besides massed combat.

I don't disagree with any of that - is there something I said that you disagree with?