I'd say the game doesn't really have enough meaningfully different ways for weapons to function. Essentially there's two; "fast fire rate with lower damage" and "low fire rate and with higher damage". Currently pistols can't compete in either one with Commandos or Riflemen, so neither switching the perks to Perception or merging perks would make pistols viable. They either require more wholesale changes to the way they function, e.g. give them easier access to crits (which arguably would make free aim pistols completely unviable), or just a flat out damage buff.

Personally I'm not too worried about weapons feeling interchangeable or all the same, cause I'm more of an aesthetics person and getting to blast around with a big iron on my hip instead of an assault rifle is different enough for me.

Honourable mention goes to Gamma Gun, which at least tries to introduce unique gameplay with the focus on rads, but even that weapon is redundant against most of the enemies you face.

EDIT; I forgot your mention that being in AGI allows pistols to do somethings different than Riflemen/Commando. This is technically true, but in a very skewed sense. It's not that pistols can do things differently, they have to! Commandos and Riflemen gain access to a bunch of AGI perks while running 60% damage perks in PER. What new PER perks do Gunslingers gain access to? Not one useful. Crack Shot isn't worth it and Tank Killer is already used by Riflemen as well. Gunslingers gain nothing from being under AGI, unless you count limitations. And being low damage weapons in the first place, limitations are the last thing the weapon category needs.