Why did 60- and 70-gun ships remain?

Why did the fleet include so many 60- and 70-gun ships instead of 64s and 74s?

Because the transition was still underway in 1759; Hawke later helped implement the shift toward 64- and 74-gun ships.

Quiberon Bay came during the transition rather than after it, so the older 60- and 70-gun ratings still appear prominently in the British order of battle. Hawke later helped implement the move toward 64- and 74-gun ships. French prizes show how wartime observation and capture fed British design and procurement choices.