To my thinking, having a reactor in the hull is considered an acceptable risk, and can have advantages in that it is more directly accessible for monitoring and maintenance. In ENT, we had a fairly straightforward reactor mated to a rather complicated "plasma accelerator" system. I assume the reason for the accelerator is that the reactor wasn't efficient enough to produce rich enough plasma to power the engines.
My thinking is that the reactors by the time of TOS are really reliable, so having them in the nacelles is no problem because they don't need much maintenance. What needs the maintenance is the energizer (more specifically the "dilithium crystal converter assembly"), so, in addition to it being unneccesary for the nacelles themselves, that one needs to be in the hull. The additional reactor in the Constitution class is there to provide more energy for the ships most demanding systems (weapons, shields and so on), to give the warp drive an additional boost and to supply the deflector dish - or, as I see it, the "high power long range sensor
(the dish) and scanner
(the thing behind the dish) assembly
That's another interesting thing. My thinking of the deflector dish is that it is not really the deflector. It's the main long range sensor.
There are ships like the Hermes class which only have the dish. Those can only "listen" into deep space, but cannot scan (like a radar). Only the ships with the thing behind the dish can do that. Ships enirely without a dish have only smaller sensors and scanners (which all the other ones have too). And the deflectors (maybe the angular shaped things to the left, right and bottom of the dish) are only added to this whole assembly, because they benefit from it (or the other way round).
By the way, I'm basing my view of the reactor system on blssdwlf
The thread: http://www.trekbbs.com/showthread.php?t=119751
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The coils probably had channels in them to allow plasma to flow inside, with the coils somehow absorbing the energy directly from them and "evaporating" the plasma in the process. I suspect that the ship's main energizers also sort of evaporate some plasma, but I suspect that the ship's power needs are generally such that the main energizers merely siphon some power from the warp plasma as it passes through the manifolds on its way to the nacelles.
I think the coils and energizers don't evaporate the plasma but simply suck all the energy out and then the plasma changes its aggregate phase back to deuterium gas. It is then pumped to the deuterium tanks or the reactors again.