CVs were only the undisputed premier capital ships in WW2 from 1943 at best. I know this position doesn't make a lot of sense given the historiographical weight Taranto, Midway Pearl Harbour etc. hold, and I'm about to go to bed so I'm not going to elaborate much but consider a few points:

1. CVs were useless in inclement weather and night operations
2. The majority of BB losses to naval aviation were on the Japanese side who had infamously useless AAA systems. Famous examples had confounding factors - Taranto was against stationary targets, Hiei had her rudder jammed, Bismarck and Force Z had malfunctioning AAA systems. The only BB losses that came solely to naval aviation were Yamato and Musashi, both of which, well you can read the order of battle for both and just realise that the odds were so stacked it wasn't anything that actually says anything about naval aviation's virtues.
3. The fact of naval combat at the time is that decisive battles between ships were rare because combat ranges had grown much faster than fire control was able to keep up. This implies therefore that CVs had value for being a more reliable way of sinking tonnage (BBs aren't shooting anything half the time!), but as established before CVs weren't sinking major surface assets by themselves with any regularity, certainly not much greater than BBs were doing.

(Scharnhorst, Bismarck, Kirishima, Fusou to BBs, Yamato, Musashi to CVs, assuming the criteria of a loss attributable solely to either surface warfare or naval aviation. Plenty of BBs were lost to naval aviation in port from CV strikes, but there were only two cases of CVs sinking underway, combat-ready BBs by themselves.)

Even in WW2, which we consider to be the heyday of CVs, the work they were actually doing was largely sinking lighter ships, providing intelligence and air cover or sinking other CVs. BBs remained something that naval aviation struggled with without support for most of the war. Why am I so focussed on the BB - CV relationship? Because the narrative around CV dominance is largely linked to this idea that they directly replaced BBs, which largely stems from a USN centric view of the war.