Well, let’s look at the head of a halberd:
It’s got a long stabby bit so that you can use it like a pike, it’s got a hook on the back so that you can use it like a bill to pull a cavalryman off his horse and onto the ground where you can stab him more easily, and it’s got an axe-blade to chop at the other person’s pole.
I think the best explanation for why the halberd was so useful is that it was the Swiss army knife of polearms, a category of weapon that has a pronounced tendency to hybridization already.
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