I don't buy it, they aren't worring about concealing them, zats are compact anyway and fold up, can be hidden quite well, don't require naquadah to operate, and don't run out of energy or projectiles.
Since the LA took over goa'uld technology and stuff, you'd think they would have been armed with goa'uld weapons.
Even when compacted, zats look quite a bit bulkier than a normal handgun, require a special holster, and are an ergonomic pain in the ****. Also, the things probably run off of a naquadah power cell, since the staff weapons have them and we have no reason to assume that the Goa'uld had some other power source for their weapons.
As for the Alliance using Goa'uld weapons, most of them suck. The only good ones are the Zats, Intars, TERs, and the Kull Warrior wrist guns. Two of them are overly specialized (Intars being stun only, TERs work only on invisible stuff), one can probably be only used by Goa'uld hosts (the Kull Warrior gun), and the I've already covered the zat guns problems.