During fights, officers and other personel have only their uniforms. without only protection against phaser fire. It would be strange that they have phasers but nothing to an officer from phaser fire.
I wouldn't be a ground troup between a phaser fire fight in the Star trek, it's just a matter of how many men you trow in a battle with phasers
They dont have armor because
Num. 1= Theres no point! a phaser set in Setting 7 (enough to kill a humanoid) could probalby blast through duranium and theres absolutely no point in armorx
Num. 3= They only make the troops less agile against the enemy
Num. 3= The armor costumes will probalby cost too much