Stability of the group being the main one (i.e. preventing it from splintering). Who ever is at the top of the hierarchy is expected to resolve the battles/differences unfolding at the lower levels to keep it stable especially when it is in competition with another hierarchy.
Will the transition work? Yes it will because we are at a point where no one individual or org has the power to dominate the network anymore. The network has grown orders of magnitude larger than any single hierarchy within it. And the pressure on each hierarchy to NOT splinter away is huge.
Just watch the guys at the top being overwhelmed. The 2008 financial crisis showed what happens when the network is threatened. It just pushes people to keep the larger network intact. It doesn't matter what their job titles are or where they individually stand in the hierarchy.
Same pressure you will see coming to bear on one Genghis Khan type character after another try to wrestle for overall control or disconnect to maintain control. Things will keep blowing up in their faces with all kinds of unintended and unpredictable consequences. Look at Facebooks fakenews response from 2 years ago to today. Look at whats happening with Brexit pushback. Look at Iran and North Korea not wanting to be isolated. Look at China realizing the impact of a trade war. Look at Saudi feeling the pressure to change. Look at Google unable to get its own employees to build a Chinese search engine.
All these are signs the guys at the top of all these hierarchies are struggling to get their hierarchies to do what they want because these hierarchies are now part of a much much larger network. And the only way they maintain its stability is to keep that network intact.
At these scales we aren't operating like a troupe of chimps or a pride of lions anymore with alphas. We resemble more a shoal of fish or a wildebeest herd. There is no central leadership.
And thats not a bad thing if you have ever seen a bunch of murmurating starlings. It will take some time for the Genghis Khan types to get with the programme though, at a cost to lot of people at the bottom of the food chain.