Actually, it's either you do all the quest chain for the lvl50 relic (which can be quite long), allowing to skip the first step of the lvl60 relic, which is fate farming.

If you are leveling up a job from 50 to 60, this is the less bothersome solution. But if you are looking to do some lore, glamour, collecting (GOTTA HAVE 'EM ALL !!), you can do either.