TOS never showed the port, starboard, midships and aft phasers, either.
How do we know that none of these phasers mentioned in "Balance of Terror" refer to phaser (bank) # 1 or # 2?
CREWMAN 1: Port weapons show ready.
CREWMAN 2: Starboard and midship weapons show ready.
MARTINE: Acknowledge. All weapons batteries ready.
TOMLINSON: Phaser one, fire.
CREWMAN: Phaser one, fire.
(Pulse phaser shots go into the darkness, rocking the Romulan ship)
TOMLINSON: Phaser two, fire.
CREWMAN: Phaser two, fire.
Because of "Phaser overload. Control circuit burnout." we never get the chance to hear another one mentioned.