Why classify a rebuilt Hood as a battlecruiser?

Could a rebuilt Hood be reclassified as a fast battleship?

On the design-lineage interpretation used here, extra protection leaves Hood within the battlecruiser category.

Hood's starting design and development after Jutland are central to this classification. Added armour and subdivision improved her protection without creating a ship from a new fast-battleship design. The modernised Kongos are treated as closer to the boundary, with some crossing it more convincingly than others. This is a particular way of drawing the categories, rather than an uncontested rule that every historian must use. A delayed-war reconstruction is judged insufficient to change Hood's lineage.