The Governing Body is a group of men who I suspect fancy themselves as modern apostles. I also suspect that if two or more of them announced that the Second Coming was going to happen on April 1 of this year you'd have a bed-wetting epidemic unheard of since...well, 1978. Great for the mattress makers.
The religion has progressively centered on them as the faithful and discreet slave of Matthew 24, though I don't know why they would want to funnel the authority to themselves. Their jobs are safe, and were safe as far as they were concerned--so why would they want the extra authority that they once shared with the so-called anointed, or heavenly, class?
As their relevance waned, perhaps they realized they couldn't take the word of those of the John-class (after all, anyone can partake of the emblems). On the other hand, power is power. David Pack, of the Restored Church of God, has consolidated it in his movement and he speaks, writes articles and views himself as an end-times apostle. The GB, on the other hand, takes a bit of a softer approach. The GB members bask in the light of authority but as far as I can tell they're not at each others' throats competing with each other for authority. They seem to be happy pulling down recognition and whatever they can get at HQ.
I'd love to talk to one of them, just to see what make 'em tick. They want to be anointed leaders, but I think some of them just lack the education and the conviction.