The new galactic government won't last long.
For much the same reasons as none of the galactic governments since the fall of the old Republic didn't last. Not only does the new Triumvirate fail to address any of the problems that have been facing the galaxy and the previous attempts at a new galactic government, but in some cases might actually be making the problems worse. Let's take a closer look at it shall we? The Three members of the Triumvirate are the Emperor/Empress of the Fel Empire, the Grand Master of the Jedi, and the leader of Alliance remnant. Each has a radically different view of how the galaxy should be governed, and without Darth Krayt as a unifying enemy threat, there's not a whole lot to prevent these old rivalries, that have left the galaxy unstable and chaotic for over a century from returning to the surface. Remember how it was the Fel Empire that was responsible not only for the rise of Darth Krayt, but the fall of the Alliance and the Jedi? How exactly are they going to be able to smooth over that kind of lingering bitterness? What about all that territory that the Fel Empire snatched in the Sith Imperial War before the Coup? Does it stay in Imperial hands or does it return to the Alliance? How do we reconcile the Imperial Monarchy with the Alliance's more republican style of government, and the Jedi's more Theocratic approach? What about the fact that the Imperial Knights are still around? Aside from the Sith, they're the biggest threat to the Jedi out there, because they have all their powers, but are loyal only to the Empire. The new arrangement is by far the least stable entity to takeover the role of galactic governance since the fall of the Old Republic.- Corellia, Kuat, Eriadu, Hutt Space, and any area not necessarily dependent on galactic government will chafe at having to follow this strange, mixed-form government and begin to assert their independence, and also reject either the republicanism of the Alliance, the monarchism of the Empire, or the theocracy of the Jedi, favoring one over the others and demonstrating why having a mixed, power-sharing government with three separate power blocs will lead to a Golden Mean Fallacy.
Legacy will get cancelled.
It wouldn't be too surprising considering Legacy's contents and the state of the Internet. George would probably get many times the backlash of the Prequels had he gone with his original plan for the Sequels. Of course, the current Sequels didn't do much better...