There were supposed to be three basic phaser settings: stun, kill, and disrupt. The highest setting disintegrates, and that was preferentially used in the show because of '60s TV censorship; it's “cleaner” if there's no body.
I don't think the TV censorship of the time had much to do with it. There were plenty of dead bodies shown in Westerns, cop shows and detective shows back then; you just saw little or no blood.
Well, yeah, that goes without saying. My point is that, in a science-fiction context where the option of complete disintegration exists (something that isn't the case in cop shows and Westerns), it would be seen as an
even better way to avoid unpleasant depictions of death.
Once again I refer to my Bible, The Making of Star Trek:
Which was a good source, of course, but no more an inviolable gospel than any actual TV series bible would be, since any offscreen, behind-the-scenes material is subject to reinterpretation as it suits the needs of an episode. And the makers of TOS were, let's face it, making it up as they went along.
Here's what the actual TOS series bible says (a passage that was cribbed pretty much verbatim by
The Star Trek Concordance):
Both the hand phaser and the phaser pistol have a variety of settings. The ones most often used are "stun effect", which can knock a man down and render him unconscious without harming him, and "full effect," which can actually cause an object to dematerialize and disappear. The phaser is also capable of being set to cause an object to explode, or to burn a clean hole through an object. In some stories we have used the phaser as a tool, such as a cutting torch.
I don't know if that "cause to explode" thing was ever used; the contents of a series bible are generally just a range of suggestions that scriptwriters may or may not choose to draw on.
Anyway, wherever I'm remembering the "stun, kill, disrupt" thing from, it's clearly not a primary source. Still, the one consistent thing is that a phaser has a range of settings, and stunning and disintegration are not the entirety of its options. Which is the answer I intended to convey to the original question.