Here's my thoughts on sights for phasers...
Starting chronologically, the EM-33, and EM-42, although not phasers, had sights. I'd assume that is because the plasma bolt they fired acted like a bullet, and arrived a fraction later than it was fired, while also falling victim to other problems faced by projectiles, like gravity, wind, etc.
Anything later than that, phase pistols, phasers, etc, did not have any sights, and I'd assume that's because the weapons fired a beam, instead of a pulse. The beam hit exactly where the weapon was pointed. And, the pistol variants of the weapons seemed to be intended for close range anyway. Most phser rifles we've seen have had sights, as far as I know.
What I suspect is that Starfleet trains it's officers to use a certain part of the weapon as the "sight", when held properly, similar to the front bead of a shotgun. There has been training like this before in our own time as well. I believe the US Army used Daisy Red Ryder bb guns without any sights to train their men in "instinct shooting". As long as the weapon is held a particular way, you can use a certain part of the weapon as a "focal point", analogous to a sight, to aim your weapon. For instance, the Type II phaser used during TNG, perhaps the indentation formed by the two raised surfaces on the front of the weapon was used as a sight. As long as the weapon is held correctly, that indentation can act as a reference point to where your shot will go.
http://www.phasers.net/2360/p2-2366a.jpg
And, practically speaking, phasers, as we have seen them used are a point and shoot type of weapon. If the weapon is on stun, as long as you hit your target, which can be accomplished by pointing the weapon at them, they'll be stunned. Regardless of where they're hit, so it seems. Same with the kill/vaporize setting used. If they're hit, they're dead.
So, I'd imagine that it's a matter of training, rather than the need to fine tune your aim. If you the weapon fits in your hand the same way every time you pick it up, and you know where your shot will go when the weapon is held that way, then there really is no need to aim. Just point and shoot.