TOS seems to lack dialogue that would associate a "bank" with a location. That is, there is no "starboard phaser bank" anywhere, is there? Just "starboard phasers" and "phaser banks", not a combination thereof.
Newer Trek does indicate that banks are associated with locations, say, in VOY "The Cloud" where there exists "the forward phaser bank". Considering the phaser emitter configuration of the VOY hero ship, though, the expression doesn't describe very well any specific individual phaser strip. It does describe a pair or perhaps a quartet of emitters capable of firing forward, though, thus possibly resembling the TOS situation, even if VOY era ships don't fire their emitters in pairs...
So there should indeed be leeway to have a "bank" power several "emitters", even if some banks are dedicated to forward emitters, others to portside ones etc. This is in fact more satisfactory terminology than having a single emitter strip be a "bank", considering how the word has classically referred to an embankment protecting a number of guns. It also caters for the meaning of this being a reservoir of destructive power, a bank vault full of death.