Sword vs. Spear

[Simetrical]

In reality, spears and polearms are vastly superior to swords even in 1vs1 combat.

Then why did so many spear-armed soldiers carry swords for backup?

When I was learning kendo, the students would use to have mock duels all the time . . . Things got even worse when the opposition held a broomstick in his hand to simulate a 'spear'. Block a spearhead? Push aside a spear? You wish. As much as you can cast the spear aside with a blow of a sword, the opponent quickly pushes it back - stabbing with the head is only a small part of spear mastery.

If I understand correctly, kendo doesn't involve a shield, which would doubtless be a great help. Furthermore, by all accounts, sword-fighting takes much more skill than spear-fighting. Finally, kendo trains you only to fight against other kendo practitioners, doesn't it? You weren't trained on how to counter spears, and neither was that kendo champion beat by a schoolgirl.

These guys can hit you senseless just with sides of the spears and that would knock a man out.

Not if you're wearing proper metal armor and padding.

-Simetrical

[Kraxis]

Then why did so many spear-armed soldiers carry swords for backup?

Because it is the perfect backup weapon. It is easily carried (try carrying an extra spear or halbard and you will understand) and it grants you the ability fight in conditions where a bigger weapon can't be used (imagine taking your halbard into the small hallways of a castle). But axes were also popular secondary weapons, depending on culture (which adds a bit to the point that swords were perhaps also chosen out of cultural preferances).

If I understand correctly, kendo doesn't involve a shield, which would doubtless be a great help. Furthermore, by all accounts, sword-fighting takes much more skill than spear-fighting. Finally, kendo trains you only to fight against other kendo practitioners, doesn't it? You weren't trained on how to counter spears, and neither was that kendo champion beat by a schoolgirl.

Indeed -do is sports, but -jutsu is the actual thing (based on the real manuals and old master to student way of learning). So if anyone have any real experience in that department then we might get a good reference.
But while the kendo people weren't trianed in fighting spearfighters, the opposite is true as well. They wouldn't be trained in deflecting a swordstrike that is feinted. So both parties would fight an opponent they wouldn't know how to fight really, but their training would certainly give them the ability to use their equipment quite well. So such a matchup wouldn't be too far from a matchup between two unproven warriors on a battlefield.
That spearfighting requires less skill than swordfighting only adds to the argument that spears are better/equal to swords.

Not if you're wearing proper metal armor and padding.

-Simetrical

Since you actually wear a metal helmet with good padding in kendo, does indicate that those spearshafts can hit very hard. The difference wouldn't be that big from a real fight. I don't hope that you thought kendo was done unarmoured... Those bokkens can break your skull and bones easily, in fact Miyamoto Musashi's most famous victory was made with a bokkenstrike to the head of his opponent. Dead on impact.