I suppose that Starfleet would not issue its officers with armour because the technology of armour and/or personal shields would not be advanced enough to absorb energy impacts or it would be impractical. Finally officers who are wearing armour may find diplomacy difficult.
The maximum setting on a Type II or type III phaser (Setting 16) can vaporize up to 500 cubic meters of solid iron. It causes moderate damage to shielded targets. Based on the description in the Technical Manual, armor would provide insignificant protection beyond what shields can provide. For reference, setting 8 is the traditional "kill" setting. Setting 16 is over 20 times more powerful.
It would seem that a single button press could change the typical hand phaser from "kill" to armor piercing "kill" with a maximum setting of "bunker buster."
Using armor would definitely increase the rate at which the enemy would deplete batteries, but the cost is unlikely justified; the benefits simply don't out weigh the costs.
Personal shields were deployed by Worf in the episode "A Fistful of Datas." Even the Borg (one of the most feared races in the galaxy) do not use armor, preferring to use adaptive shields.
The game "Star Trek Online" has introduced several different types of specialized armour, as well as "Personal Shields" [partially mentioned before]. The armour varients are designed with specific enhancements (e.g. energy resistance, kinetic damage resistance). The personal shields are designed to absorb energy but are also variated (e.g. extra capacity shields, extra regenerative shields, mobility shields). Of course, the armour is designed to be energy weapon resistant and designed to work with the shielding. It also has a built in secondary shield so that it doesn't just get vaporized. There is no point in what we would consider armour, as pointed out in the previous posts.