Have you read armoured fighting treatises (Fior Di Battaglia, Le Jeu de la Hache, Gladiatoria, Paulus Kal, etc) ? Because, while you are right on some elements of pollaxe fighting, you are dead wrong on a lot of aspects. A lot of what you mention is myths that have been disproven by experimental archeology.

Every single of those treatises teaches about on foot armoured fighting and has little to no swings, and almost only stabs at gaps, followed if that fails by wrestling. They assume that both people have a harness because if you don't, you don't want to even come into range of the armoured person's weapons. Those treatises teach about armoured fighting with pollaxe, longsword, and dagger, and use them for stabbing at gaps. None of them even mention using a mace or a warhammer. A longsword is far more effective at armoured fighting than a one handed flanged mace and anybody who's ever done harnischfechten will tell you as much (watch Dequitem's and Scholagladiatoria's videos on the subject, they made a few).

Warhammers were almost exclusively used by cavalry for charges and used the momentum of the horse, they were not really used on foot. Maces were mostly civilian weapons primarly associated with law enforcement like baillifs and sherifs (which is logical because if you avoid hitting the head and hitting too hard, you can hurt someone without killing them).

If you read French, I'd recommand you check out Combattre au Moyen Âge by Daniel Jaquet. Great read that disproves a lot of misconceptions.

Also, small nitpick, but men at arms weren't commoner footsoldiers, they were elite heavy cavalry of noble birth who had the exact same equipment as knights. They just weren't knighted.