The Intrepid class is a great fit for scientific research on the fringe of Federation space.Well the 2nd computer core, could be a back-up core with enough funcationality to get the ship to the nearest starbase.
In that context it's only logical that she'd have redundant systems where one set could be dedicated to keeping the ship running and on course while the other takes care of a the mission itself.
Think in terms of how the bridge and the CiC aboard a modern warship are both control centers which control ship-wide systems, but take care of completely different aspects.