Well, the first answer that springs to mind is “why did they keep unretiring the Iowa-class battleships?”, with the answer being “because sometimes what you need is a heaping helping of fire support”. I note that the serious complaint about those battleships was never that the big guns weren’t useful; it was that they were old, expensive-to-upgrade ships with high crew requirements, which made them not useful enough .
But consider these historical differences:
One, there was never quite such an, um, definitive set of historical events to emphasize the beginning of the Carrier Supremacy Era. (i.e., Pearl Harbor, Coral Sea, then Midway). Also, they were rather better than the USN was, historically, at integrating aircraft carriers into their doctrine as major combatants pre-Pearl, so the CV/BB one-two punch theory was already out there.
Two, they’re rather tougher than in our timeline. Because spinmetal, which if you recall the Invincible-class fast battleship, they used in limited quantities for citadel armor. Well, that was then, when the process involved mining limited and irreplaceable deposits of it. By the time of the Invictus-class battleship (and thus the Laurë Isilvieré-class battlecarrier that was based on it), two generations of ship designs later, they’ve figured out how to breed spinmetal, and so can afford to lavish this remarkably strong (aramid-varietal yield strength) and relatively light metal on their armoring schemes, as you can see from the description of the BV’s armor up above.
One of the big contributors to the death of the battleship was that it doesn’t take a lot of anti-ship missile to kill a ship, and quite often just one will do it. Well, now imagine that the armor is approximately an order of magnitude better . Just like in the old days, you have to batter them to death, unless you’re down with breaking out the atomic shells. A lot of the time, even if you do break out the atomic shells. This takes time and mass.
Three, they’ve got bigger, longer-range teeth. In our timeline, when the need for surface combatants reared its head again in the 1960s, the answer was the guided missile cruiser and, slightly later, the guided missile destroyer - because we’d already, see one, obsoleted battleships.
Once again, back in the days of the Invincible-class fast battleship, the 14" powder guns were the primary armament. Two generations later, for the Invictus-class battleship, the 16" coilguns are still counted among the primary armament, but a fair assessment would say they took second place to the fuckton of VLS cells prepared to open a Macross Missile Massacre-flavored can of pain on anything that wanders into Sarissa range at a moment’s notice.
Which is to say, they put the missiles on the battleships because they were already the major surface combatant class, so why change? Also, a battleship has a lot of room for VLS cells.
They just don’t bother labeling it a BBG, because all BBs of its generation would need the G, as would the CCs and DDs. (Same as the lack of N.) The distinction is that the CCs and DDs tend to stock defensive anti-air missiles in their VLS cells, rather than the general-purpose/anti-ship Sarissa.
The combination of two and three means that the CVs take enough time to kill the opposing battle group that it can close the range more, and the missiles (primarily) and coilguns (secondarily) mean the BBs don’t have to close the range so much before engaging.
tl;dr Two equivalent battle groups closing on each other will start out tearing into each other at aircraft ranges, but if they don’t choose to disengage, will at least partially survive long enough to brawl up close.
Additional note: also, the laser CIWS coming into fashion in this era will hopefully detonate and/or break up incoming missiles before they hit, but won’t do a hell of a lot to a big ol’ shell, much less a solid k-slug.
Further additional note: And, y’know, from a Doylist perspective it provides more interesting naval battle scenes than “surface fleets are missiled to death by over-the-horizon aircraft in a battle lasting maybe five minutes”.