Limited firing arc doesn't really mean much of anything when you're firing from Range 100-150 - they also have low rate of fire, so they have plenty of time to swing the bow of the ship around to the next target before it's ready to fire again. Tracking also isn't an issue, as X-slot weapons aren't intended to be used against Evasive targets, and Battleships have four other L-slots' worth of weapons for the Evasive stuff.
One of the problems that Stellaris has is that, while you have four weapon sizes and four ship sizes, the progression isn't even at all. Corvettes are able to mount both S- and M-slot (equivalent) weapons, Destroyers move up to comfortably carrying M-slots and expanding into L-slots - that would suggest that Cruisers should center on L-slots and expand to X-slots, while Battleships should be pretty much focused on X-slots across the board and maybe something bigger beyond that. But that's not what we have: Cruisers completely top out at L-slots, and Battleships can only have forward-fire-only X-slots, not turrets.
I think part of the reason for this is that they decided to have sections with limited portions of the weapons load in each - Corvettes only have the one section and Destroyers are 2/3 vs. 1/3, but both Cruisers and Battleships only have 1/3 of their hardpoints in the Bow, 1/2 in the Core, and just 1/6 in the Stern. The M-slots in Corvettes and L-slots in Destroyers take up 2/3 of the hardpoints by themselves, but oddly these aren't viewed as spinal cannons when maybe they should. In order to justify an X-slot on a Cruiser, you'd have to pretty much do away with separate sections and instead just have a whole-ship blueprint to allow for the outsized spinal cannon.
The other part is that, if you have Corvettes with S-slots, Destroyers with M-slots, and Cruisers with L-slots, and there is a beyond-size-increase boost to damage as you go up in size, Battleships "should" be doing not just twice as much damage as Cruisers, if they only have L-slots, but an additional 20% beyond. If only 1/3 of the weapons can account for that additional damage, then they have to do even more extra damage to average out. If Battleships could just get X-slots in 3 mounts rather than just one, the DPS for X-slots could be more in line with regular slot size increase progression.