I can actually see a secondary control center in the saucer in TOS Star Trek. Unlike the TNG Enterprise, which was essentially two fully functional ships docked together, the TOS Enterprise was not. If a Constitution class starship had to perform a saucer separation, it was an extreme emergency situation and the engineering hull and warp nacelles were simply discarded. Now if the saucer was that catastrophically damaged then the crew would take to the escape pods, shuttles and/or transporters to find safety. There is additional tactical value in having the secondary bridge in the saucer, if the bridge is rendered unusable or captured by hostile forces, the command staff can retreat to the secondary bridge and take measures to reestablish control of the ship from there. This could be as simple as activating the controls there, in the event the main bridge is destroyed or deactivating the primary bridge controls in the event of hostiles occupying the main bridge.