They made a design choice of a cinematic 30fps with movie like letter-boxing.
Of course this would free up resources so they could use better AA.
I am in no way saying the engine could achieve say 60fps or that quality of AA in full screen but I do believe as stated above it was a design choice not a console limitation and you haven't showed this not to be the case yet.
Yes, I have -- to be clear, the reason the black bars are there is because they wanted to maintain 2.40 (cinematic ratio) and they couldn't achieve 2.40 fullscreen along with 4xMSAA. That would have required a render target of 2592x1080p w/4xMSAA @ 30fps. That would get you the cinematic "feel" as well as a clean image and no black bars. PS4 couldn't handle this. So they included the black bars (1920x800p) to reach their target.