I do agree it SHOULD be a fundamental in sword fighting, because it is
Sorry, forgot to address this one while I was ranting ...
Good edge alignment is not vital for sword fighting. It is vital for target cutting. Swords were created specifically to cut human beings, and they are terribly efficient at it. If I were to cut any part of your body with a poorly aligned sword cut, it would still be devastating and debilitating, and you'd most likely bleed to death from it without immediate medical intervention.
Getting close enough to cut your opponent without being cut yourself. THAT is what's fundamental in sword fighting.
P.S. That video showed horrible form. He needs proper instruction in cutting.