Why the Royal Navy considered 9.2-inch station cruisers

Would 9.2-inch cruisers appear when battlecruiser guns increased to 13.5 inches?

Yes, once large battlecruisers became too costly for global station duties; the smaller ships fill a different role rather than competing directly.

Fleet initially rejects a large 9.2-inch cruiser alongside battlecruisers, while Alex Clarke distinguishes its overseas station duties from capital-ship work. Early Invincibles were close enough in cost to armored cruisers that building both types made little sense. As battlecruisers grew into Lion, Tiger, Renown, and Admiral-scale ships, the Royal Navy could no longer afford enough of them to cover its worldwide stations. The replacement burden included 101 older armored cruisers and pre-dreadnoughts used as station flagships and for deterrence, conflict management, and other peacetime duties. A 9.2-inch cruiser could retain the status and fighting power needed for that work without acquiring capital-ship costs. Increasing its guns to 12 inches would also sacrifice a rate of fire suited to cruiser operations. The Hawkins class was not considered an adequate replacement for those station flagships.