Battlecruiser, fast battleship, or battleship?

Would the G3 class necessarily have been the Royal Navy's last battlecruisers?

Not necessarily. Future choices would depend on how the Royal Navy balanced strategic mobility against armour, subdivision, and fleet fighting strength.

Battlecruisers are built around strategic mobility, while battleships emphasize strategic strength. A fast battleship seeks both. It accepts design compromises to combine speed with the protection and subdivision needed for fleet combat. British phrases such as fully armoured battlecruiser show how fluid the vocabulary could be. The operational problem a ship was meant to solve is often more informative than its class label.