In the original planning, there was a plan to have a parallel taxiway for the second runway. However it was dropped because
1) The way the runways are normally used because of the spacing between them - landing on 05R or departing on 23L doesn't require one. A parallel taxiway is only required when landing 23L and departing 05R which doesn't happen often (although all this summer whilst R1 is fixed but at night-time only when traffic is generally lighter)
2) A parallel taxiway would require much extra land take, a much longer tunnel over the river and A538 and the cost could not be justified with so little regular use and no capacity gain in normal operations.
3) Bearing in mind the above and the planning climate, it was decided not to proceed with it.
Who knows whether it will ever be resurrected - I guess not in the foreseeable future anyway
I agree in that it might not have seemed cost effective at the time of construction of the 2nd runway to build the parallel taxiway the entire length. But it would have been a great deal cheaper to have built it then at the initial construction phase rather than add it on now or in the future.
Sadly the bean counters took control of the planning. Before the move north, chatting to a number of my colleagues up in the tower, many commented that it would make their work easier if there were a taxiway to the far western end of 23L.