The fact you never touched FFXI aside, Fame does this:
-Unlock Quests/Missions
-Adjusts vendor prices (this is why crafters are suggested to get high fame, more return profit)
-Makes NPCs react to you different (kind of hypocritical to say people want a dynamic world but will shit on an idea because it came from FFXI)
-FFXI wise, it allowed you to extend your inventories.
Only people who say it was "boring" or "tedious" were the group of people who thought you only get fame from repeatable quests and never went past rank 2.