Why Australia and New Zealand received battlecruisers

Why build battlecruisers for Australia and New Zealand when a more powerful design was available?

The battlecruisers were affordable enough for the Dominion governments to pay for, making finance central to the design choice.

A more powerful British capital-ship design does not answer who would pay for it. The battlecruiser option was inexpensive enough for the Australian and New Zealand governments to fund. That shifted part of the imperial naval expansion away from the British government's own budget. The procurement choice therefore joined combat capability to Dominion affordability and political willingness to purchase a major warship.