tl;dr- Individual characters shouldn't be granted access to uncommon weapons, uncommon exotic weapons should become uncommon martial, and GMs should be given the authority to make common weapons uncommon.
The Exotic Weapon Problem
Simple and martial weapons make enough sense on paper. Simple weapons are straightforward enough that anyone can pick them up. For example, jab your opponent with the pointy end of the spear. Meanwhile, martial weapons take more training, so you have to specifically learn to use one with Martial Weapon Proficiency. About half of the classes get a few martial weapon proficiencies for free. And martial classes are skilled enough at fighting to be competent with whatever strange weapons they may find. But then there are exotic weapons, which mostly fall into one of two groups, both of which have strange to negative implications.
The first type of exotic weapon is the accidentally-too-powerful kind. For example, the elven curve blade is almost entirely an upgrade to the normal greatsword. It's lighter, finessable, and threatens critical hits more often. The only downside is the slightly lessened damage dice, 1d10 vs 2d6. This is effectively gameplay and story segregation. The concept of martial characters getting all martial weapons is that they're that good, but these weapons are too powerful from a game design standpoint, so they have to be locked off.
The second type of exotic weapon is the more concerning one. Weapons that don't fit in a pseudo-Medieval-European setting like most of Avistan. I could get into how WotC and Paizo both have a habit of raiding the thesaurus to expand weapon tables, like how the only difference between a gladius and a longsword is that the former apparently gets the crowd more excited, but that's not what this is about. If you accept that wakizashis, katanas, and nodachis are sufficiently different from shortswords, longswords, and greatswords to warrant different stats, I could understand a paladin from Absalom only knowing how to use Avistani longswords and not Tien katanas. But if I head over to Minkai and make a paladin... she's still familiar with Avistani longswords and not Tien katanas. Even Tien characters need Exotic Weapon Proficiency to learn them, because apparently martial characters are specifically familiar with Avistani weapons. The samurai class mitigates this somewhat by providing proficiency in wakizashis, katanas, and naginatas, but still leaves two questions. One, why wouldn't an Avistani samurai just use Avistani shortswords, longswords, and glaives instead? And two, what if a Tien samurai wanted a two-hander? The only options would still be using an Avistani greatsword instead of a Tien nodachi or to take Exotic Weapon Proficiency to learn a local weapon.
The only weapons I can think of that are actually more complex are Numeria's lasers and Alkenstar's way-post-Medieval guns.
Common and Uncommon Weapons
Entering 2e, Paizo definitely seems to have noticed the unfortunate implications of that latter group, and just made them uncommon instead. Martial characters actually know how to use every weapon now, and it's just locked by setting, which weapons are available. Except there are a few problems.
First, there are still a grand total of 4 exotic weapons. So the first problem I mentioned still exists. If we already have this tool to let GMs restrict access to weapons, why do fighters still need to learn those four weapons individually? If you have an uncommon weapon class, there should be no need for exotic weapons.
Second, item rarity should be determined on a setting level, not a character level. Using the example of Tien characters and katanas, suppose my Minkaian paladin travels to Absalom. Theoretically, katanas are an uncommon weapon there. But because they were specifically granted access to the weapon, there's apparently some secret Tien black market that this character and this character only can access to find katanas. Or similarly, if an elf with the Elven Weapon Familiarity feat goes to the Five Kings Mountains, they'd apparently find some secret elven black market to buy an elven curve blade.
And third, there are no provisions for converting an item to uncommon instead. This follows off the previous point. If I set a game in Minkai, I could grant everyone access to Tien katanas... but they'd also still have access to Avistani longswords, which are theoretically less common in Minkai.
The Common/Uncommon split actually can work in theory to solve both halves of the exotic weapon problem. Just not with the current implementation.
The Weapon Proficiency Problem
This is a separate issue, but continues off things mentioned in all that explanation. In 1e, characters bought proficiency in singular weapons, unless they took a level in a martial class. But in 2e, the Weapon Proficiency feat just upgrades you to the level of martial classes, being proficient in all but 4 weapons in existence. You can then take the feat again to learn individual exotic weapons. This has two issues:
First, all of those "simple plus some" classes are now irreplicable. Why does a Bard only know certain weapons, but if my Sorcerer wants to learn to fight with a rapier and pretend to be a Bard, he has to learn to use all martial weapons with it? And second, if I want my character to specifically learn to use firearms, which would presumably be exotic, they'd have to learn all martial weapons first.
Additionally, there's the issue of fighter weapon groups. These technically already existed in 1e, but they were specific to the class. But now that they're tied to the TEML system, it introduces a third way you can gain proficiencies. On a per-group basis.
Thus, I also propose a change to weapon proficiency in general. Everyone is trained in simple weapons, and instead of giving martial characters all weapons and most other characters a handful of specific weapons, you let each class pick so many weapon classes to be trained in. The Weapon Proficiency feat would be gaining training in another weapon class. The fighter class abilities could be gaining training in a handful. And you could even extend the system to have thematic options, like forcing clerics to pick their deity's favored weapon's group or gunslingers to pick guns. This is actually simpler than the current system, because you don't have to deal with martials and characters with Weapon Proficiency getting everything, but exotic weapons being taken on an individual basis and some classes starting with specific martial weapons. Weapons would effectively just be skills like Athletics or Thievery. And it protects future weapons like firearms which do deserve the exotic name, without having to make a separate system to gain proficiency in them.
