The "problem" is that the Watchtower Society was "manned" (yes "manned" - the only woman who featured in the early days of the organization got viciously pummeled in writing by her ex-husband, Chuck Russell) by men who obsessively believed in themselves, had grandiose senses of their importance in the Divine scheme of things and who appeared to genuinely believed that the end of the world/system/whatever was so very close that it was not necessary to explicitly and formally arrange for successors in the event of the President's death. I
It is the stuff of religious groups the world over. Think Roman Catholicism and the behind-the-scenes grapples for power when the Pope was on his death bed. It brings to mind the maxim, "Too heavenly minded to be earthly minded" or, in the case of the Watchtower Society, "too caught up in personal interpretation of Scripture to notice what's happening right under their very noses".
Rutherford was as much of a religious jerk as the seemingly cuddly Chuck Russell - only Rutherford was undeniably more prepared to be openly ruthless and nasty. Chuck hid his nastiness behind flowery words and woolly denials. His ex-wife certainly saw this daft white-bearded man for what he was: Duplicitous and narcissistic.