Another important point is that it is easier to aim a thrust at the joints or gaps in armor than to aim a cut at them. Hard to swing a sword edge under the armpit of your enemy to go around his breastplate.

Weapons like warhammers or maces that were designed to break or dent or just deliver force through armor without aiming at the gaps were generally swung to generate more brute force. A thrust at the face through the openings in the helm needs to be more precise, but doesn't need to be very forceful at all.