This doesn't contain spoilers. It isn't really important to the plot, really. It is just a theory that evolved as I wrote, and I guess, it is mostly for fun, and to maybe give a theoretical backbone to the AU of my fic. Still, it might be interesting to read, so I'll leave it here.
Before the royal family, 'shadow' energy permeated everywhere, 'shadow' and 'light' energy coexisted, for the most part evenly, various creatures, peoples used these energies, mostly for simple spells, nothing too overpowered. some trained in them and traded in energy work. (Nemek, Eamond, the Garo) some creatures or people were intentionally or not, 'afflicted' or containers of the energies many 'monster' forms are the way they are as evolution to the energies that were part of them eventually, some people started to monopolize, hoard large amounts of the energies, in tools, talismans, or in themselves as living vessels the sheikah, Rauru, the royal family did this to an extreme degree. Rauru and some sheikah made themselves into vessels, weilding then great power, but they wanted more - they concentrated shadow energy into a golden talisman, so much energy, that the talisman itself was unstable, the Triforce, so named because the only way to maintain it was: every few generations, it is split into three parts, which are placed into three vessels, allowing the energy to cool down for some years during this time, there would be a power vacuum, so precautions must be taken to ensure continuity of rule the vessels must be made in such a way that, they will safely contain the energy, not fall into hands other than the royal family, sheikah. chaos must be created, the pieces hidden, with the people too concerned with survival, to try to take any of the pieces of the triforce. During the cooldown phase, the pieces of the triforce will likely "steam off" energy, Link has to kill various monsters, use various magic, in order to dissipate this excessive energy in his triforce piece zelda's excessive triforce energy, is used to create the sages, which are containers, which will themselves let off some steam, but destined to eventually be reuinted. Ganondorf's excessive triforce energy, causes the destruction of land around him, monsters to follow him or spawn from him, After some time of cooldown, the three pieces can safely be reunited, but the re-fusion process is costly, one of the vessels must be sacrificed - ganondorf