I don't think so. TOS had a pretty good mix of warp vs warp and warp vs sublight battles
"Balance of Terror" - Enterprise (warp and sublight) phasers at Romulan (impulse)
"Balance of Terror" - Romulan (impulse) plasma bolt at Enterprise (warp)
"The Ultimate Computer" - Enterprise (warp) phasers at Fed ships (warp)
"The Ultimate Computer" - Fed ships (warp) phasers at Enterprise (warp)
"The Ultimate Computer" - Enterprise (warp) torpedo at Woden (unknown)
"Elaan of Troyius" - Klingon Battlecruiser (warp and impulse) at Enterprise (impulse)
"Elaan of Troyius" - Enterprise (warp) torpedoes at Klingon Battlecruiser (warp)
"Journey To Babel" - Enterprise (unknown) phasers and torpedoes at Orion ship (high warp)
"Journey To Babel" - Enterprise (sublight) phasers at Orion ship (sublight)
"The Changeling" - Nomad (warp and sublight) torpedo at Enterprise (warp and sublight)
"The Changeling" - Enterprise (sublight) torpedo at Nomad (sublight)
"The Deadly Years" - Romulans (probably warp) torpedo at Enterprise (warp)
I would have to disagree.
Balance of Terror
…The Enterprise fired at warp 2 into open space
(couldn’t get a lock on the Romulan). This is essentially the sci fi equivalent of dropping depth charges. The Romulans speed was never mentioned, only that her power supply was the same as what powered the E’s impulse engines. The Romulan torpedo is in fact a warp speed capable weapon as the Enterprise backed away at full emergency warp and was still overtaken; one of the few actually confirmed as warp capable.
The Ultimate Computer
…the Enterprise was at warp in all cases, but the targets of her weapons were never specified as being at any particular speed. You can only make assumptions but they are just assumptions.
Elaan of Troyius
....in this one the Klingon strafed a sublight Enterprise until the Enterprise went to warp. The Klingon was at sublight on the last battle pass as Sulu counts the range down at about 10,000 KM per sec or so. The Big E then pivots at warp two and apparently drops back to sublight as it was another ten or twenty seconds before she fired on the sublight battlecruiser.
Journey To Babel
....in this episode the speed of the Big E is not confirmed. The attacker is at a much higher speed but that’s all we have.
......the Enterprise speed is never mentioned. The episode is a mishmash of conflicting information concerning Nomad's weapon speed and range.
The Deadly Years
….in this one, the Enterprise was at sublight before Kirk came back onto the bridge and ordered the ship to go to warp speed.