Battleships sided aircraft carriers for two reasons: one was to thicken their inner defense ring a little, and the other was because battleships alone, without a friendly air wing to keep the other side's strike aircraft away, were doomed.
20% better at 3x the cost is usually a bad bargain in a battlefield increasingly dominated by dispersion strategies and that was what eventually killed the Battleships, they were to expensive for convoy duty and too slow and vulnerable to torpedo and air attacks for the line of battle fighting that actually happened doing WWII.
Only because neither the US nor the Japanese had carriers in those engagements. The writing was on the wall when the Brits crippled the Italian gunship fleet with a single obsolete aircraft carrier in 1940.
It's hard to say for sure, but in a way it seems that the Hood and the Prince of Wales actually stood a much better chance of causing serious damage to the Bismarck than the Ark Royal did, even if that's not how events happened to play out. (And in fact damage from the Prince of Wales's guns did help to slow the Bismarck down and force it to attempt to go to port to refuel.)