Treknology and TMoST
tend to be mutually exclusive: basically everything the book ever suggested, online developments have proven incorrect. Luckily, phasers still remain a vague technology, not easily contradicted one way or another..
Scotty: "I can adjust the main reactor to function with a substitute fuel supply."
Spock: "That's all very well, but we don't have a substitute supply."
Scotty: "Aye, we do. Our phasers. I can adapt them and use their energy."
The interesting thing here is that the original fuel was a fluid stored in a tank, probably gaseous or cryogenic because when leaking out it disappeared without leaving a puddle. But Scotty said they lost it all when a leak indeed developed - yet after the phaser trick, there suddenly is fluid in the tanks again! Or at least something that can be measured as "fifteen pounds psi" (a nonsense measure that was probably meant to read "15 psi", a valid measure of pressure and useful for gaseous fuel being stored under pressure) and sprayed out to create a light show.
Do phaser batteries store energy in fluid form? Was Scotty draining gas
out of them and into the shuttle tanks? The shuttlecraft also had "batteries", and those were used for electrifying the hull and repelling the savages - plus "boosters" which seemed to spray out gas and generate thrust in the process. These were clearly different systems from each other, and from the main power or propulsion system, the one that used the fluid they lost in the leak. It's a jumbled mess...
...And certainly enough to make this particular phaser-draining trick "ad-libbed" even if getting power out of phaser power packs in general were the most routine thing in the world.