I'm not an anarchist, so I cannot speak for them, but I think the point was more of whether is was possible for anarchists to be able to manage the commons. Whether shaming etc. is preferable or not doesn't matter as much. I think many anarchists are just fed up and would rather figure out a way to live together without a system that is easily corruptible (govt). Even if it means using techniques that aren't preferred.
RE: Should anarchists abolish the commons?