It does raise the question of how to solve a murder involving a disintegration if there were no witnesses. By the time someone's reported missing the evidence may have blown away.
It also raises the question of why no more murders are performed that way. Why was there a corpse left in "In the Hands of the Prophets"? After being shot with a phaser AND placed in an active plasma conduit! Is it just a question of the murderer trying to avoid triggering the weapon sensors at the murder location? (But DS9 doesn't seem to have much in that department.)
The TNG Companion suggests that money/time was indeed the big issue in the diminishing number of disintegrations, not audience sensibilities. See the entry on "Face of the Enemy".
In-universe, we might say that disintegration uses more power and thus is not used much in wartime, but that Starfleet people use it as often as possible in peacetime because it's more humane than burning holes in the victim's chest. Or that it requires some fine-tuning to achieve a good kill without going for all-vape, and TOS era phasers lacked that finesse.
Timo Saloniemi