It's hard to imagine that pedestal being a major part of the ships power system, because there's no way he could open it without getting blown away by either, electricity, plasma, or anti-matter. It must be tapping of some minute amount of power to do something, but what. And what is it that can be fixed by fiddling around with it?
"Getting blown away" wouldn't appear to be a problem, intuitively. To make use of this access point, Spock first has to enter a protective compartment of some sort and then unscrew a cap. Clearly, protection is being taken care of! That is, if the dangers of the power core can be accessed somewhere, this is obviously it.
The idea that this is the terminal for a dumbwaiter system that moves the dilithium into the reactor focus down below for use, and back up for repair and replacement, would appear to cover all the bases. Dilithium is the one thing that can be helped by "aligning" in explicit technobabble, and dilithium is closely related to "mains" and "energizing" as well. Spock is just twisting back a crystal frame that has been bent the wrong way by Khan's hits.
We never actually hear this shaft referred to as an intermix anything. The original Enterprise, in my opinion, had three reactors, one in the engineering hull controlling the other two in the nacelles (the glowy domes). Perhaps this three reactor system was replaced by a single reactor in the refit. I think that the glowy blue dome near the impulse engines is new matter/antimatter reactor. The shaft we see is actually carrying the output plasma from the reactor down towards some energy systems and out back towards the nacelles. So there really isn't any intermixing happening in that shaft. Just some thoughts.
I'd be the happiest with Kirk's ship having a system consisting of
all the parts we ever see, simultaneously - even if those parts come from slightly different timepoints, parallel universes or whatnot.
That is, I assume the system works the TNG way, because the system worked that way in ENT already. I also assume there is a big spherical reaction chamber somewhere beneath Scotty's usual workplace, generally inaccessible except through this dilithium dumbwaiter and other waldo rigs. A dilithium focus there handles the annihilation of matter and antimatter from tanks that perhaps surround the top and bottom of the sphere, respectively, making good use of the space. An ejection system doubling as a refueling hatch is clearly marked in red and yellow on the outer hull, beneath this assembly. All sorts of pipes take the produced energy to all sorts of locations for all sorts of uses, sometimes requiring a "transformer" such as the warp field manipulation crystal doodad that makes the warp field reduce the ship's inertial mass for better impulse maneuvering, sometimes entering the appication "raw"; the transfer medium always is plasma, filling the pipes and perhaps slowly circulating, and not being constantly produced and immediately expended (although occasional purging is typical). And we see a major main power trunk and its nacelle-feeding branches in TMP, now more "naked" than before even if the ripping out of the vanity covers also means Scotty has to wear coveralls more often, but we still don't get to see the heavily shielded reactor underneath.
Did I forget to integrate something there? Dilithium may be in the form of big crystal lumps, but usually Starfleet has to make do with industrial dilithium dust, in a paddle-like matrix that has to be cuddled back to energized status, that is, the dust facets realigned, in a special chamber if something goes wrong. More advanced power systems can energize the dilithium on the spot, though. The ship is also dotted with all sorts of auxiliary reactors, probably fusion-based ones, for which the minimum number is four so that the three sometimes mentioned have to specifically pointed out as this subset of exactly three, rather than as "all of 'em".
Oh, and big beer tanks and man-sized pipes for water absolutely feature in there somehow.
Timo Saloniemi