uses one to power the cargo transporter.
Which was pretty darn cool I thought, and was a first in Star Trek
And which brings us full circle: If a hand phaser holds enough juice to power at least one human transport, then surely it holds enough juice to power half a transport and beam someone out of existence.
It's not a question of raw power.
The only technical issue with whether the phaser works that way is in the nature of the beam itself; does it have the right kind of emitters. A distinction between what we saw on TOS and what we saw in TWOK with dematerialization was that in TOS, the setting seemed to freeze the victim in his tracks. Of course, the color was a pale and ghostlike and hardly suggested flames and burning, also in contrast to TWOK. The OP's question is hardly a dumb one.
No residue or scorch marks were left on decks. I'm going to admit that until TWOK, I thought the TOS dematerialize was always a conversion of matter to energy, because the victim seemed to simply disappear. What we saw in ENT: In a Mirror, Darkly, Part II,
was a retcon.