Makes perfect sense, and is a great example of an easy-to-use weapon custiomization system that allows the player to tweak the performance of a favorite piece of equipment. I'm not much of a CoD player, but I'm a big fan of the gun addons in it (less enthusiastic about the grind to unlock stuff). You can't put a grip on your rifle that boosts your HP or anything silly like that, but you can do enough for the gun's attributes that my FAL and my buddy's FAL might be filling different roles in the arsenal.

Fully customizable statistics is what I want.

This is certainly the way to go in most RPGs or Turn Based Strategy Games.

Although to do this well, you would still need rules so the player doesn't end up with a severely weak character because the player put too many points in the charm stat and not in the combat stat. Or, they find an exploit and turn their character into a god.

I prefer to have "modifiable skeletons". The skeleton is a weapon type (rifle, shotgun, spear etc.) and then you can add stuff to it. Either as temporal buffs (5 seconds of double damage), spatial buffs (extra damage if fired from a certain region), permanent buffs (which cant be removed). I guess there are more types out there. But the most important thing is that it should not be possible to affect the core balance. I remember crafting a ring in Bethesda's Morrowind that killed anything in the game with 1-4 "touches". A weapons upgrade system should merely add some "flavor" to a weapon, not change it in its core.

An alternative way, if the weapons are high-tech, is to add an adjustment score to the weapon. The player can then adjust how the energy of the weapon should be guided: speed, power, accuracy etc. depending on the situation. Then you can add more "adjustment points" to the weapons with upgrades.

I think I have more fun choosing weapons as a means to 'upgrade' my ability to kill.

It was fun back in the nes era Dragon Warrior to come to the next village and invest in either:

A - The stronger weapon (and keep money for armor, potions, etc).

or

B - The uber-master-much-much-stronger weapon

This has obviously evolved a lot, but I still find value in how simple the economy ties with having a 'better weapon'. Its also how I feel I do things in real life:

I don't refit my car, I buy a new one when I've got the money and the need. I 'upgrade' from condo to house (I don't turn my condo into a house).

Likewise, I purchase a gun if I want to kill someone, I don't refit my kitchen knife into a potatoe propeller (wait what?)