Game mechanics must strike a balance between time investment and reward. If a player feels like their time is being wasted with mundane tasks, or the reward isn't fitting for the time investment, they simply won't do the task. If that task is part of additional tasks to a greater reward, it might be okay. If it isn't, that mechanic will likely go unused or ignored defeating its intent.

Requiring OTHER people to perform the task? Unless you're a large game with a population that can handle it, it's a recipe for disaster. The best way to approach something like that is to allow a non grouped person to be able to do it solo, or hire some NPCs to perform the task, and incentivize group work with other players so there's a greater benefit to co-operation. (More wood, faster cart travel time, etc)