The location of the bridge, as well as of the battle bridge, is also an interesting metaphor for Starfleet as a whole: the main bridge is out in the open, which is good for negotiations (it can show that you have nothing to hide, which could help make others more amicable), but the battle bridge is buried deep inside the ship, where it's less vulnerable to weapon fire. This This is a reflection of Starfleet's stance on combat: while peaceful exploration is their main goal, they're ready for a fight if push comes to shove.