Nigel (and others),
Your faith in the logic of the Birmingham management's decision-making is very touching! There are a number of reasons why BHX may have opted for a runway extension over (say) more terminal space or parking areas, not all of them logical.
The first, and most obvious is that the runway extension was probably first considered well before the 787 spec was firmed-up. The expectation then was that long-haul meant long runways, now not so important.
The second was that initial planning would have taken place prior to the financial crash/recession that we and much of the rest of the western world, have been suffering for five years. In those days, long-haul flights and holidays were in greater demand, people (thought they) had more money, and air traffic was increasing everywhere.
It is not unknown for management teams to suffer from hubris - the thought that they and their business is more important than it is by objective analysis. I'm sure this played a part in the BHX runway decision, augmented by its close cousin, local pride. ("If MAN can get long haul, so can we - we are a bigger city").
I would be very surprised if the expenditure on the runway extension is ever commercially justified. The idea that flights to China are merely five years away is fantasy, I'm afraid. BHX suffers from its proximity to London - and always will. Yes, there is scope for some long-haul, but not much. An analysis of current long-haul operations shows a couple of transatlantic routes - not much changed over the years - and services aimed at the significant immigrant population and their descendants visiting their ancestral home countries (PIA, Air India, even Emirates and THY).
Sorry for the reality check!