This seems to be a variation on a very old argument regarding the nature of the 1701's power source. Lines from the show can be interpreted to mean either power generation in the nacelles or in a central reactor. For my money, I interpret them to mean that there are three reactors, one in each nacelle as a more or less dedicated power source for each warp engine and a central one which powers mostly the ship but is somehow critical to keeping the other two operational. So why would this be so only on the TOS Enterprise but not the later (and for that matter, earlier(NX-01)) ships?
Simple. The engines of the NX-01 did not require near the energy as later engines since it wasn't as powerful. The warp technology could of outpaced the reactor technology making 1701's engines huge power hogs (after all, warp 8 is 512c while warp 5 is 125c; about 1/4 the power). But if the reactor only got twice as good then obviously a single power source would not have been sufficient for such big engines. Eventually (TMP) breakthroughs in reactor technology did catch up and the centralized reactor came back into vogue.
To the original question as to why the core is so far from the engines, recall that this "warp core" is merely the giant D-cell that powers the ship, warp drive included. It's not simply a dedicated system for just the engines, even though, doubtlessly, there is no single system that uses more of the power it produces. It makes sense to put it as near the engines as it is, but there's no reason it has to be right up there with them.