The funny thing about "The Ultimate Computer" is that maybe Kirk did subtly alter Daystrom's request.
Daystrom wants it hooked to directly to the power plants (like the matter-antimatter and/or fusion reactors)
but Kirk instead tells Scotty to hook it into the power banks
(like the main energizers).
DAYSTROM: Thank you. Thank you very much. Captain, I've finished my tests on the M-5, and it must be hooked into your main power plants in order to be operative.
KIRK: Well, by all means, do so.
DAYSTROM: Your engineer there wouldn't allow us the power necessary without your orders.
KIRK: Mister Scott, hook in the multitronic unit to the ship's main power banks.
And later on M-5 does find a way to get also
hooked into the warp engines and the matter-antimatter reserves... So it was getting both the main power bank energy and the power main power plants energy, too. Virtually unlimited power
This differentiation with plants and banks occurs also in "The Doomsday Machine" and we hear Spock say:
SPOCK: Allpower plants dead, reserve energy banks operative at a very low power level.