I'm inclined to disagree. You're right though, that Westeros is not very authentic in this regards but swords have been favored historically too despite their relative weakness against heavy armoured enemies.
a) Swords and lance were historically considered the knightly weapons while Axes and maces etc. were considered unknightly.
b) In europe swordstyles had been developed to fight plate-armoured enemies and swords developed into some kind of thrusting instead of slashing weapon.
Maces and warhammers actually got used more often as plate became more advanced, and quite often were considered "knightly" weapons. Unique sword tricks were used to piece armor, but these swords were large. The kind of sword Jon Snow ends up using is the kind of sword nearly everyone used when plate was invented, called a bastard sword in Britain and just a longsword everywhere else (because it was really long, not medium-sized like many swords), and the techniques for beating armor involved "half-swording" and almost using the weapon like a spear, not a sword, and most notably involved a two-handed grip, while many Westerosi seem to heavily favor usage of shields, probably because the "longsword" described in the book is more of an arming sword, which got used quite a bit with shields.
Though I note that in most of the battle scenes, many characters DO seem to be using much heavier weapons then a simple sword: Loras Tyrell is mentioned to he using a morningstar, Robert has his big-ass hammer, and greatswords are all over the place. Many of the characters using regular swords end up drawing them when not