The 2-handed flail (ie the pole-flail) missing from weapon lists.

Swords have Long swords and Great swords.

Axes have Battle axe and Great axe.

Blunted have Warhammer and Mauls

Then you jump to polearms, mostly assumed to be halberd, glaive style  (leaving out Lucerne Hammers, reaper/battle scythes and others), Trident should also be more of a polearm rather than just a different spear.

But flails are only assumed to be the short handled, short chain, weighted blunt/piercer (and yeah, you should be able to chose damage type!) leaving out the pole-flail (2-handed) completely left out or for homebrew, but why?  These would be great cleric or pali weapons. 

In a lot of ways, i think the weapon categories were overly simplified, for example yes a Lucerne Hammer (mentioned above) is not overly different from halberd other than damage type. Katana can be grouped with long swords, etc. but then you have more specialized weapons that sorta don't fit to the given "types". Parrying Daggers/Knives are longer blades, not typically good for throwing because they would typically have better hand protection. The Scissor is a bladed weapon, but also armor (also for game play a stat like "can not be dropped" or something.). There are evolutions of Rapiers that give them more of a blade (slashing not piercing) that still maintain light, finesse, elegant weapon craft. 

And why oh why, are Scimitars listed at a heavier weight (3lbs) in the game over Rapier (2lbs), but THEY have LIGHT, where Rapier (by your own admission) a lighter weapon does not?

Trident is a spear, because spears can be one handed in the rules, and Gladiator movies showed Tridents and Nets as a weapon pairing, and no exclusively 2handed weapon has the throwing property.   You can thank/blame Hollywood for that.

The Light property leans into the concept that they well suited for Dual wielding.  The length and weight of the Rapier are due to them being modeled on Fencing swords; hence they are finesse and piercing. 

Trying to argue realism and history in a game based on fantasy and movie tropes is a fast track to proving you're not paying attention to game design.  Failure to account for game design is a good way to lose the argument, because it would result in something that doesn't make sense in the context of the game rules.  Flail is half the weight of the Mace, and yet it does more damage, even though both weapons is you swinging a stick with metal on the end. Logically the mace should do more damage because it has more inertial.  And Long swords should have Graze, since you can thrust with it, and the edge can still cut an enemy you didn't stab; while Greatsword should have Cleave, and Great Axe should have Eviscerate, and Halberd should have Topple, and Glaive should have Vex.  

And none that would matter anyway, because a Gun should be doing 5d6 damage and at least 3 attacks per round.  

and as a thought..... should pole flails be simple weapons, since peasants can use them?  Or should they be martial because they require training to use?