That's what I wish they had done in the first place, really. It woulda been so easy! Say that every time Link travels back in time during the course of the game, he splits the timelines. Traditionally in a time traveling video game those timelines are just discarded by the plot, but they coulda said that the LTTP branch grew out of one of those "abandoned" timelines. The sages need to all be activated, so it could be some time traveling he did before the end of the game but after all the dungeons, and since he doesn't really think about the consequences of time travel, he doesn't particularly realize that these timelines are being orphaned without him, left to Ganon's machinations. That last one with all the active sages could still seal away Ganondorf like Hyrule Historia says they do, and boom, LTTP branch all set up.
But nope, instead we have this dumb "Link was defeated" pap. I can only hope they one day flesh-out/retcon it into something more like what I described.