I am not sure the words "warp core" or anything close to it were ever uttered in TOS.
TAS: "Beyond the Farthest Star" mentioned the "engineering core," but that's about it. And in
Forgotten History I made sure to avoid having any 23rd-century characters use the term "warp core," instead using terms like "warp reactor" and "engine core." (However, "warp core" was used in the 22nd century in ENT, so theoretically it could've been in use in the 23rd as well.)
In context? So we ignore the possibility of techological evolution?
On the contrary. TOS is bracketed in time by ENT and TMP, both of which had internal warp cores. So the conjecture that the
Constitution class had the same is a reasonable one. Also, there are only a few years elapsed between TOS and TMP, and the seemingly revolutionary change in technology between the two has always struck me as a bit jarring, so one of the things I like about Drexler's cutaway is that it smooths the transition by having TMP-like elements in the TOS-era ship. I am considering evolution, because a gradual transition between two similar forms is a more plausible evolutionary path than a drastic and wholesale change in a very brief period.
And no, I'm not "ignoring" any possibility. It's good to consider all the possibilities, but ultimately you have to choose one over the others. That doesn't mean you ignored the alternatives, just that they didn't win out in the end.
My point is, that we have concrete examples for TOS where they specifically mention that the nacelles generate power (eg "matter/antimatter nacelles"), so to ignore stuff like that is to take out the context and insert present (TMP-TNG tech). Something that was phyically and visually quite different.
But the context is not just one show, it's the whole 45 years of canon. If we're pretending that there's any cohesive reality to the Trek universe, then it follows that we should consider the whole. If you're talking about TOS as a fundamentally separate creation from everything else, then you're talking about it metatextually as a work of fiction, and in that case there's no point having this discussion because we can just dismiss it as a bunch of sets and drawings.
And yes, there are inconsistencies in the whole. That's a given in any long-running canon, especially one created by so many hands over so much time. But since it's all pretend anyway, that means we can pretend it fits together. That's what the makers of the canonical productions do -- either they ignore past references that conflict with their current interpretation, or they try to reconcile the whole as best they can and disregard the details that don't fit. Anyone who interprets "canon" to mean "truth" is missing the whole point. A canon is a fictional construct, an illusion of reality. The details are always subject to interpretation and change as part of the process of developing the illusion.
So yes, there were some early references to the engines being in the nacelles. Those were decades ago, they were a consequence of the early creators making stuff up as they went, and there are many, many years' worth of subsequent creativity that takes things in a different direction. It's just like the early inconsistency about lithium/dilithium and what purpose it served, whether Spock was a Vulcan or Vulcanian, and things like that. It makes more sense to me to go with the preponderance of evidence and not get hung up on the growing pains.
Anyway, it's all supposed to be entertainment, just a fun creative exercise. Nothing worth arguing over.