I'm somewhat reluctant to now say that the impulse power system has nuclear fusion reactors that generate power now
But that's exactly the beauty of nuclear fusion reactors. They will produce energy (hopefully put into better use that what we're envisioning for the "steam engine era" we still live in) or
A fusion rocket
is basically a fusion reactor with a valve that functions as an engine nozzle.
... due to the instances where they would've been handy such as "The Naked Time" and the ability to rapidly exhaust the impulse reserves under load which strikes me more of a "battery" issue rather than fusion reactor issue, IMHO.
Because of the "exotic" gravity effect of Psi 2000 and their advanced stage of orbital deterioration they needed warp power. This had been made clear earlier, when impulse power was only the second choice:
SPOCK: Gravity pull increasing. We've shifted to two percent and should stabilise our position.
KIRK: Helmsman, stabilise position.
BRENT: Helm is not answering to control.
KIRK: Warp us out of here.
BRENT: No response from engines, sir.
KIRK: Impulse power then.
Blast us out of this orbit.
BRENT: Impulse engines also dead, sir.
Later, Scotty was able to fix their impulse power: "Engineering to Bridge. Try your helm. You'll have enough (impulse) power to keep her stabilised."
But at this point their orbit had deteriorated to a point where it was only possible to "stabilise" but no longer to "blast out of the orbit".
It was imperative to use warp power which they finally managed. The problem was not the lack of fusion or impulse engine power but how to use the fusion power to heat up the antimatter and/or the engines to perform warp drive, IMHO.