Everything had to be working in order to be Cat 3. Often, an aircraft would be Cat 2 only, or even Cat 1 only, due to a u/s component.
You couldn't guarantee that every Trident would be Cat 3 capable on every day.
Even then, if the skipper didn't quite see the lights at 12R, the P2 would immediately go-around, and in later years consideration for the passengers' nerves would preclude more than two attempts (think Double-Echo accident).