Now this is the mysterious thing: phaser beams are virtually never "walked" onto their targets. (Indeed, the only successful instance I can think of is from "Arsenal of Freedom" where a trio of heroes deliberately "caged" an enemy to prevent it from maneuvering, then swung the flanking beams to join the center beam at the target. Klingons swinging their disruptors in ST6 is not an example of successful use...)Constant beams can be "walked" onto target if the initial aim is off.
In contrast, despite the absence of any sort of sighting devices, the phasers fairly accurately hit targets that the user has had at least a moment to contemplate. That is, if you jump into view, then dodge out, the phaser may miss you. But if the phaser user has enough time to take aim, there will be a hit, regardless of whether the user actually did take aim. Apparently, the sidearms do the aiming by themselves, or at least fine-tune the initial coarse aim to ensure a hit.
Why don't they "walk" the beams? Perhaps there is massive inertia in doing so. That is, the beam might not be a mere ray of light (as pretty much everything about their behavior speaks against them being that), but rather some sort of an "energy rod" connecting the gun and its target, and while holding the "rod" takes no more muscle power than holding the gun, swinging the "rod" strains your muscles to the extreme. Alternately, the beam is a conduit that takes some time to establish, and if you keep moving it, it never settles and never allows the actual deadly energies to flow from the gun to the other end.
Apart from that, I undersign that the phaser does appear superior to anything we have or plan on having today. No doubt Trek-level technology could produce even better weapons, like the Tantalus field that forgoes messy gunslinging and simply makes the enemy go away, but phasers really are pretty good weapons.
Except for snipers: the beam immediately gives away your position, and it moves at a snail's pace, probably allowing your victim to dodge it if he stands more than a hundred meters away. Plus we don't know if the thing has a range limit. The Gorn did some pretty good sniping in "Arena" from tactically significant distances, perhaps but not necessarily with phasers, but all other such action has been at close quarters.
Timo Saloniemi