Here the difference between a cut and a piercing weapon is smaller, but still, most effective ways of hitting these areas involve thrusts of some kind. Now, things are a bit different for steel plate armor, as that can't be (reliably) pierced the goal is instead to find weak spots like armpits and inside of the elbow and the face, which are usually protected with mail or just padding instead.
A pike may burst your mail and gut you, if there's enough force behind it. It slightly alters the bladed combat, and it changes the way a swing does damage when you attack on horseback.
It improves a wide variety of Mound & Blade functions. An arming sword basically can't hurt you on the covered areas, at least not with a swing. Once you have compulsively played your 200 hours of Mount And Blade, you may try their most popular upgrade, which is Mount And Blade Warband. So consider you're wearing a mail over a padded shirt.
That's really what the flangs on a mace are primarily for - making the weapon grip rather than glance. Blunt/percussive weapons on the other hand, leverage a lot of force that doesn't easily glance off, transferring that force into the person under the armor. That's not the rationale - it's that piercing weapons can (under the right circumstances) penetrate armor - maybe not plate, but mail or cuir boulli or similar armors.
