On the precise term "intermix" you are correct.
The related terms are "Intermix Ratio", "Intermix Chamber", "Intermix Forumla"
Which are throwaway technobabble to which no physical object has ever been canonically tied. It is not established whether the "intermix ratio" or formula have anything to do with the intermix
chamber. For all we know it's a ratio of reactor coolant to de-ionized water that have to be mixed before delivery to the warp core's heat exchanger.
Memory Alpha assumes otherwise.
Memory Alpha, being a wiki-software website, does not have the agency to make assumptions. That's for PEOPLE to do.
All other references to intermix are warp drive systems.
Well, they're ASSUMED to be warp drive systems, or related to them in some way. Again, nothing has ever been pointed to on screen with the words "intermix chamber," it could just as easily be a fancy type of coolant system, all our assumptions notwithstanding.
The Phoenix, The NX-01, Arctus Baran's ship, The Enterprise D (Galaxy Class), and Defiant. All these vessels have warp drive. All vessels these references are to faster than light systems.
The listed reference in phoenix is just for its engine components, not a warp drive component. It's telling that we don't even know what the intermix chambers look like on any of these ships, let alone what they actually do.
Your quote is ambigously offered to warp drive...
No, it's EXPLICITLY offered to impulse power. And the fact that the warp engines weren't working at the time because of "antimatter imbalance" clearly indicates the antimatter reactor system was not operational. If anything, this tell us that "intermix" is not
necessarily part of the warp drive.
I think what it is...is that in the 24th century the core has been combined with the intermix chamber.
Indeed. Just needs to be established that what's true of the 24th century is not necessarily true of the 23rd, 22nd, or 21st.
We know that the intermix has everything to do with plasma flow, fuel control for anti matter and matter reactions.
Again, no. We simply know that the intermix chamber is a device that is very important for modern engine designs. We have NO IDEA how it relates to antimatter systems, or even if it is necessary for them, or even if it can work without them. We at least know from TMP that sometimes it CAN work without antimatter. This being the case, the Phoenix can also function without antimatter.
The switch that is flipped is clearly marked "Warp Core."
Fine. Show me a switch that says "antimatter injector" or "dilithium crystal status" and you might have something. Otherwise, there's no evidence that the warp core had any resemblance of any kind to its TNG/ENT counterparts, and circumstantial evidence--the time period and scarcity of resources--to suggest a very rudimentary, very primitive design using neither material.
You might as well suggests that the Wright Brothers powered their first flight with a turbofan engine and a fly-by-wire navigational computer.
I propose that the very mention of a warp core and intermix chamber is a direct relationship with antimatter/matter reactions.
And you suggest wrong, as already demonstrated that the presence of an intermix chamber has NO implication for any particular power system.
Even if it was just Fusion system I am incredulous of the possibilities of anything short of a large scale organization with resources and abundant materials putting together a Rocket Test Vehicle combination out the first try.
Cochrane clearly didn't have that kind of organization, so it's a non-starter. More likely he was just a crazy old man with an equally crazy idea that just happened to work.