So yeah, to give exotics a name you'd have to redefine the proficiency concept first.
Is it a matter of skill and familiarity? If so what about applying the same level of skill to a simpler weapon? What about similar weapon skills? If it acts like a club, should not the skills carry over?
The existing system seems to indicate so, since martial weapons tend to be more tricky to use without specialized training. However, other than the really far out exotics, most of them work just like simples and martials, they're only exotic because they're foreign.
Is it a matter of weapon quality? Simple weapons are generally cavemen weapons, with low requirements on construction, or dual use tools and hunting devices. Martial weapons tend to be purely military in nature, and meant to kill people effectively. Going by this order, exotics should be even more effective, perhaps weapons ahead of their time. But then you have the whip, which other than its reach, falls cleanly into a simple weapon(its a dual use tool), the kama(which is an oriental sickle), and so forth.
Personally, I'd make it a matter of skill and weapon groups, forget 3 tier weapons. You're proficient in types of weapons, and focus to get higher effective rank in a weapon category.
Rank 0: Untrained unarmed strikes, natural weapons
Rank 1: Clubs, staves, spears, daggers, repurposed farm tools(the common scythe, whip, sickle etc), basic unarmed strike(nonlethal but non provoking, think simple boxing)
Rank 2: Swords, advanced unarmed combat, flails, scourges(whips with metal knots) stuff that takes training to use properly,
Rank 3: Advanced techniques for Rank 2 stuff, weird hybrid weapons,
And you keep going up with more weird weapons and advanced uses of lower rank stuff.