If a quest/task/puzzle does nothing of following it should be removed
1.Introduce the player to specific gameplay mechanic(these quests must be optional to not annoy veteran players playing for the Nth time)
2.Advance the storyline or fill in game lore(optional and only if "lore" is large/dramatic enough - i.e. no small infodumps).

In general its better to minimize amount of quests/tasks/puzzles unless they are really vital.

The side quests/fetch quests/daily quests/task-quests should not exist in a well-design game, because they structure the gameplay into work. Useless quests detract from game overall quality, making its atmosphere conceptually simplistic(i.e. it creates impression of game being ruled by simple concepts like task->reward, instead of complex picture that emerges from player vs the world interaction: a task->reward quest reinforces the player impression of game being routine work). Task-Reward quests should be minimal/optional at least, not harming character development.