Actually Battlecruisers were a part in a hugely complicated plan to lure both sides into the decisive battle fleet encounter.
Today we can't imagine that, but a set piece naval battle like Jutland was every bit as formalized as a medieval joust.
Light forces gain initial contact, call for backup. If light forces are destroyers like at Jutland, backup is cruisers. Cruisers call for backup themselves if outmatched, which are the Battlecruisers. These fight aside the enemy screen and ultimately sight the enemy battlefleet, keep contact and vector own battlefleet towards it. Of course in doing that they ran into their own counterpart, which happened at Jutland and went quite badly for the RN.
Lighter forces like destroyers were to be kept back until the tactical opportunity or necessity for a mass torpedo attack arose.
Before the advent of the aircraft, every ship short of a battleship was mainly a scout.
In the 1930s, the US heavy cruisers were officially still the "scouting force" of the US Fleet, like the imperial german battlecruisers had been officially designated the 1st scouting squadron.
This role only became redundant with aircraft and aircraft carriers.
You're right that "raider killer" was a role of RN cruisers in WW1, but it was not their envisaged role, and in the 1920s the world's admirals (except the french and germans, and the few soviets) had come to the conclusion that WW1 was an abberation and the next naval war would be Tsushima all over again. In WW1, german battlecruisers or even light cruisers lacked the range to do raiding. Actually any capital ship raider with coal firing was doomed to fail sooner or later for sheer logistics.
So the actual role the Lexingtons were designed for was to scout ahead of the battle fleet, fight aside the Kongos and Akagis (which were designed as Battlecruisers) and shadow the IJN main force so the US battle squadron could destroy them.
The IJN pretty much thought in these terms, hence the whole pretty useless "distant cover groups" the IJN employed in nearly every battle without any useful purpose.
The only WW2 battles that were fought along that recipe were those in the med between the RN and the Italians, and those mostly ended in mutual (not cowardly italian, as mostly claimed) retreat because no side could gain any advantage.
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