It seems just as likely that Nomad's tampering provided a major leap for the Enterprise's propulsion, and important clues for the future. Nomad stated that it had "increased engine efficiency by fifty-seven percent", and there's no reason to disbelieve that.
We seem to forget, though, that Enterprise still had limits in flight...
I disagree that TOS Year 3 suddenly showed the Enterprise bounding about under her own power at Warp 9-plus speeds all the time. Consider "That Which Survives":
This establishes that the Enterprise's "top warp speed" is still Warp 8. And a little later...
So, Scotty coaxed "a wee bit more" and gave Spock Warp 8.4.
We seem to forget, though, that Enterprise still had limits in flight...
I disagree that TOS Year 3 suddenly showed the Enterprise bounding about under her own power at Warp 9-plus speeds all the time. Consider "That Which Survives":
SPOCK: Mister Scott, since the Enterprise is obviously functional, I suggest we return to our starting place at top warp speed.
SCOTT: Aye, sir. But even at that it'll take a while to get there.
SPOCK: In that case, Mister Scott, I suggest we start at once. Can you give me warp eight?
SCOTT: Aye, sir. And maybe a wee bit more! I'll sit on the warp engines myself and nurse them!
SPOCK: That position, Mister Scott, would not only be unavailing but also undignified. Lieutenant Rahda, plot a course.
RAHDA: Already plotted and laid in, sir.
SPOCK: Good. Then prepare to come to warp eight.
This establishes that the Enterprise's "top warp speed" is still Warp 8. And a little later...
RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.
So, Scotty coaxed "a wee bit more" and gave Spock Warp 8.4.