Actually, you're proof that it's herding cats. We both see the same on-screen information but we come to different conclusions
I beg to differ. Compared to the average treknological interpretation of the TOS Enterprise's
power infrastructure I do feel our conclusions to be remarkably compatible, especially since we (seem to) agree / assume that nuclear fusion plays a more significant role than usually accepted.
It's the details from which we draw different conclusions and if I understood correctly you consider the possibility that warp drive is possible with nuclear fusion only, where I do agree except that it would require nuclear fusion energy to be either amplified or converted by dilithium crystals and mixed / integrated with the m-am annihilation plasma ("intermix formula"). In "Elaan of Troyius" we do not seem to see the ship running on battery power (to extend the duration of their interplanetary voyage), yet warp drive capability has been sabotaged because the dilithium converter assembly has been "fused".
I'm not entirely convinced the SS Valiant
had warp drive. The whole premise in "Where No Man..." is astonishment how that ship got to the edge of the galaxy, until it's disclosed that this ship "encountered a magnetic space storm and was being swept in this direction" (could the ship have been sucked into a wormhole which in the 1960's would have been called "magnetic space storm" for the lack of better terms, available then?).
Even if it would have had warp drive the "magnetic" space storm might have rendered warp drive correction pointless so the ship had to rely on its old impulse engines to break free, which however and according to Kirk weren't strong enough.
Where I also disagree is to assume warp drive capability for the Romulan Bird of Prey in "Balance of Terror". This was not established in the episode (Scotty: "Their power is simple impulse" - and no warp drive)
and the star chart suggested Romulus and RomII to be in close (interplanetary) proximity to the Neutral Zone. For all we know the return voyage of the ship could have taken months or even years.
Apparently, by the time of "The Deadly Years" the Romulans had refitted their fuel pods with warp engines, possibly as a result of the unholy Klingon-Romulan Alliance we learned about in "The Enterprise Incident".