i think that this may have been an over reaction to the fact that modern airliners are not that easy to slow down and most of them will not slow down and go down at the same time.
At the time the Trident was being built most of the aircraft flying with the airlines were props or turbo props and when you put a propeller into fine pitch at speed it acts like a very big speed brake , I can only think that it was invisaged that the Trident needed to match the braking performance of the other trafic.
The landing gear speedbrake was only fitted to the 1E so it sujests that it was found to be an unnessesary complication and so omitted from later aircraft.