Well, this ducks the cost that ZRun mentioned. In game firearms are expensive...and so is the supply of practice ammo that would be required to learn the rapid pace of fire you describe.
During the Napoleonic Wars, which was the absolute height of regimented firearms, many soldiers were given less than a dozen practice rounds to shoot. The majority of work was drilling, and instruction; But even then, that was second to instilling discipline in the ranks. The act of learning to use a black powder weapon was elementary, and could be effected with ease, if you were made familiar either by proximity to them, or simple militia drilling.
Another example of this would be American Colonials during the American Revolution. They did not have very much in terms of supply at all; But then again, casting a bullet was the easy part. It was acquiring the black powder, that was the more difficult of the two; Which required to be mixed to a certain standard.
You have to load the powder and bullet. A firearm also has to be cleaned and maintained. (I don't know why a rapier would be historically more expensive, but that's irrelevant to which costs more in the game.)
Finally, the more you argue that this is so "infamously easy" the more you make the case anyone should be able to do it; in other words, it should not require a feat investment for others either.
Should picking up a bastard sword and swinging it need exotic proficiency when one is proficient in the long sword and great sword? I suspect the reason it does is for game balance. And for game balance firearms should be just as difficult or easy to learn, regardless of a character's domain of origin.
The case made is for people for whom martial weapons proficiency would apply, ultimately; The racial/origin trait suggestion was just a way to implement it that seemed more feasible. Arguably, not every Dwarf would be proficient with their waraxe, nor every Elf with a Longbow, which took much longer to learn how to use, and by historical standards, the building of much muscle in order to utilize a longbow with a draw strength effective to harm armored foes.
A sword of any form, requires someone who is a skilled smith to balance, temper, and smith it. It then requires an understanding of how to use it in order to not immediately die in your first fight. One can pick up a sword and swing it around, but to use it with any effectiveness, requires years of practice. As evidenced by the numerous historical manuals recovered and placed in museums depicting maneuvers, concepts, and practices of swordsmanship.
Firearms are very easy to use, by comparison; Easier to use than a Crossbow, and far, far easier to use than a Longbow. The most dangerous part of doing so is seating your powder and priming the weapon without putting too much powder inside, but this issue was resolved by pre-measuring powder into paper or wax cartridges, which is also a thing they do on PoTM, the item exists. Tools also exist to pre-measure powder for shots, that work to the same effect that frontiersmen and hunters would use, those who would carry powder horns.
The process is simple. You measure the powder, either with a device, or a paper/wax cartridge. If the latter, you pull the hammer to half-cock, you rip the paper/wax cartridge it, pour the powder in the frizzen until full (that's the pan beneath the flint), close the pan, pour the rest down the barrel, push the paper/wax cartridge down the barrel with your thumb, grab the ramrod, push it down until it can't go down any further, return the ramrod, pull the hammer back, aim, and squeeze the trigger. Someone with an afternoon of instruction or who watched it occur could do it with consummate ease, especially if they grew up in a world where it wasn't an uncommon sight.
Take a Longbow, for comparison; In an age before compound bows. You would need to get a bow that matches your draw strength, and then knock an arrow, and loose it. That sounds easy, except for if you've ever taken archery with a recurve bow, you know that the muscle groups used in archery require development, and in order to be an effective archer, you need to spend hundreds of hours practicing. In the case of a firearm, aiming is just pointing in a general direction; There is no precision aiming in a time before rifling.
Take a Crossbow, for the next comparison. A light crossbow requires you to place it down, put your foot in the brace at the front, grip the crossbow back until it's cocked and try not to pull it unevenly, then place the bolt, and loose. Very ease, but also requires you to be able to pull the weight of the crossbow. Crossbows that could be pulled by hand were ineffective in warfare because of plate armor, for the most part; So by the time Crossbows became a weapon of war, they were often accompanied by a rope-and-pulley system that you had to mount upon it, wench the bow back, and then place the bolt and loose.
Then, finally, the sword. You can point and stick, and swing a sword, but to do it with any likelihood of surviving, you have to use it a lot. If the feat means, Proficiency, then to become Proficient with a sword would take a lot of practice against an instructor who will teach you the maneuvers of swordsmanship, or numerous fights against other people from which you could riskily learn.
Now come back to the pistol. You don't need much. And cleaning it out is another conversation, but the side-effects of failing to clean it out can be underlined in the Careful Handling feat, rate of fire in the Gearling Feat and Delven's Maneuver Feat. Firearms are given more feats in complexity than Crossbows, despite Crossbows being somewhat more complex and cumbersome in their operation than a firearm, especially the Flintlock, which is what made the Firearm easily accessible to everyone, and operable in most conditions.
Had this been a Matchlock, it would be a different story compared to the Crossbow, which is why during the 1500's and 1600's when Matchlocks were a thing, Crossbows still saw great favor in the battlefield and among armies. Wheelock pistols were used by the rich and affluent, because they allowed for pistols, and because they didn't have to fiddle with a lit match (a burning piece of hemp rope) in order to function. Flintlocks were the keystone to making firearms the universal weapon for armies, because their operation was simple and relatively foolproof, except for inclement weather.
Now, my argument towards familiarity with the Dementlieuse vs. Others, is that Dementlieuse are around these things all the time. Firearms are their national image of a mainline weapon of war. Gendarmes carry them on their belts, Thugs use them indiscriminately, Hunters use them for game, Levies raised are drilled in their usage because it's easier, cheaper, and a direct counter to the aged Falkovnian method of warfare. In-fact, you're raised in Dementlieu to believe that the superior Dementlieuse way of warfare is the only reason they aren't chattel to the KingFürher.
Compare this to say, Barovia, where firearms and black powder are prohibited. There is no nation in the Core that has such a relationship to firearms in their national identity, as Dementlieu does. Therefore, it doesn't make sense that firearms would be anything approaching exotic to them.
Now, one can argue that it's for some measure of game balance, and while I might timidly agree to some extent, from the perspective of the roleplay, that is where I disagree. After-all, one can easily outperform a Flintlock Pistol in DPS, even on a Black Powder Avenger, by investing half as many feats into a Longbow and using high-end Alchemical ammunition.
With that, I've said all I could; I'm going to bow out. It's obvious this isn't a popular suggestion.
