It feels like there is actually a super easy solution for energy that presumably wouldn't make people upset. Let people reincarnate into 10 year bodies, die, then keep their memories and bring em back. At that rate basically everyone is immortal and moebeus keep getting energy. The only things bad about the system is that they have to fight for no reason and that they don't keep their memories, except when they do in colony omega, and also keep their bodies that already become husks, but were somehow unhusked, or something?
As a fundamental matter of thermodynamics, there really isn't a solution for energy within the paradigm Moebius established. The fundamental concept of "let people kill each other, then reincarnate them, then repeat, all while skimming a little life energy off the top to sustain ourselves" is a closed system out of which Moebius keeps siphoning energy, which means it will eventually run out because of the first law of thermodynamics. Whatever tricks are employed to improve the speed at which life energy can be harvested (as was happening in Omega or that colony where everyone is a first-termer), they're never going to be able to get out more energy than was involved in creating those lives in the first place. While it's never explicitly stated, I expect this is part of where the annihilation events come in: By turning large volumes of matter into energy, the deficit is fixed and the world can continue to function, though obviously this is still a finite solution.
That said it's really never implied beyond an outside understanding of physics that that is the case. In-game, it's implied that annihilation events are a consequence of the parallel worlds being held in stasis just before they would have naturally annihilated, and they happen when too much of one world leaks through into the other (as indicated by the black fog, which arose for similar reasons in Future Connected). This is where the power of interlinking comes from (for both Ouroboros and Moebius): It taps into the power of Origin to bring entities from the two worlds closer together than they otherwise could get, releasing significant amounts of energy by holding them just on the brink of annihilation. This is also why there's a time/energy limit, since that state can only be maintained for so long before the pair collapses in on itself and annihilates. I've seen some other theories that talk about the black fog as an autonomous natural entity that tries to erase dimensional abnormalities, such as the remaining Telethia (pieces of Zanza, who shouldn't exist outside of the memory space that Xenoblade 1's world occupied) in Future Connected, but I'm not sure if that means the black fog causes the annihilation events or is just associated with them.
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