Another reason for vertical geometry might be cooling issues. As was stated above, a starship creates it's own artificial gravity and, in the show, artificial gravity has been proven to be very reliable. It seems to remain working, even when everything else does not.
Thermal convection needs only heat and gravity to work and it doesn't work very well horizontally. So that method might be used as a backup to keep the coolant circulating if the pumps stop working for some reason. Might not be enough for a warp core running at full power, but should work for removing the excess heat after emergency shutdown.