Your and others' arguments are convincing, I will change my vote, even though it probably isn't needed at this time.Nope. Here's the logic:
1) This isn't a primary combatant; if it's outnumbered (by foes it doesn't grossly outclass anyway) it's just going to warp away, and the aft phaser is useless.
2) This is a maneuverable ship; if it's not outnumbered, it's going to be able to keep its fore armament on target, and the aft phaser is useless.
The aft phaser would only ever make a significant difference in two circumstances:
1) Fleet actions involving very large numbers of ships on both sides, such that despite its maneuvers keeping its prow to its immediate foe, there are just so many foes that its aft phaser randomly happens to bear on a target often enough for its damage to add up.
2) Facing multiple opponents that it could handily outmaneuver, but which it overmatches in toughness and firepower by only a small degree.
Even if this somehow makes it out of the yards in time (which I'm still skeptical of), scenario #1 might happen once or twice in the entire Four Years War, and will never happen again for the lifetime of the ship. Scenario 2 will literally never happen against the Klingons, at least. The Klingons don't have light cruisers; their combat-capable fleet jumps straight from the light frigate Bird of Prey to the D-series, which despite its higher tech and lower mass is best thought of as a straight-up battlecruiser.
This ship- regardless of aft phaser choice- is likely to end up with enough firepower and shield strength to take apart single Birds of Prey despite their modest maneuverability edge, if well-handled. It's highly unlikely to take the fight to multiple BoPs, who could likely pick it apart with good teamwork- it'll run away at warp. So it doesn't need the aft phaser against lone BoPs and can't use it against multiples.
It's seldom if ever going to need its aft phaser against a lone D7, as it (slightly) outmaneuvers them and should have little trouble keeping its fore armament on target. It does have significantly weaker shields than the D7 or its true peers, and might well end up needing to flee one at Warp if the opening exchanges go poorly (rendering its aft phaser useless), and will absolutely be fleeing multiple D7s at Warp (rendering its aft phaser useless).
Now if the Gorns or Tholians or whoever are given to punchy light cruisers or heavy frigates in about this weight class with slightly-inferior overall tech and no more than Medium-High maneuverability (you know, the sort of thing this ship might actually want to fight more than one of solo), or if we're facing a foe that definitively outsprints us in the Warp that we can't flee regardless of aft torpedo, then sure, the aft phaser might come in handy. I still don't think it'll be handy enough often enough to be worth the 4 cost, though. I mean look how far out I had to go to find a circumstance where it would be useful AT ALL!
Eh, their shield tech is quote-unquote "nakedly superior" to ours- they have grossly stronger shields than we do for ships of the same mass. We do generally outmass them by enough it's kind of a wash, though, yes.
Another advantage of no aft phaser is it'll make the cost of a rapid fire launcher less crippling. Pricey but compelling.