Why use 28 knots as the fast-battleship threshold?

Did the definition of a fast battleship keep rising with the speed of each battlecruiser generation?

No. The classification used here begins at roughly 28 knots, rather than rising with each new battlecruiser generation.

In this classification, about 28 knots separates a true fast battleship from a faster super-dreadnought. The threshold does not rise each time a new battlecruiser enters service. It explains why the hypothetical 28-knot Queen Elizabeth receives a different label from the actual class.