I figure that with the approach of the Dominion War, and the resulting more militant stance of Starfleet they were replaced with the type II as the standard sidearm for more power. The type I would be more for concealed carry, diplomatic security, etc.
They practically disappeared long
before Starfleet ever found out about the Dominion.
I tend to think it's a battery thing - the only reason to carry a Type 1 over a T2 is if you're trying to hide the fact you're carrying a phaser. But, y'know, any alien race worth its salt will scan for phasers with a tricorder-type instrument if they're concerned about it, so there's little point unless you're dealing exclusively with a pre-warp culture. Which you shouldn't show a phaser to because of the Prime Directive.
So, ultimately, where's the advantage in carrying a mini-phaser that has a smaller battery and thus fewer shots over a not-exactly-huge standard phaser?