Remember: the sages must be awakened in order for the failure line to even make sense. Consider the town names from Adventure of Link. Only Link could awaken the sages. He was necessary for that. The failure line must branch from Link's duel with Ganon in Ocarina of Time.
If Link was not needed for the sages to be awakened, it wouldn't be called the failure line. If Zelda could presumably do so, Link would never have been used.
If Link was not needed for the sages to be awakened, it wouldn't be called the failure line. If Zelda could presumably do so, Link would never have been used.