It's not so much that you need to use violence to stop people from privatizing the means of production, as much as that you don't use the authority and capacity for violence of the state to enforce private property rights. In the absence of a such a threat of violence, abolishing the privatization of a community resource can be put to a vote, and then you can just not respect this person's claim to private property. If no one respects the claim, it doesn't exist. Until such a time as this can be achieved peacefully, we are not ready to live under anarchism.
Capitalism creates an imbalanced distribution of resources by enforcing a certain set of property relations. It isn't a law of nature. Like Gandi said, poverty is a human invention that can be abolished by humans.
Everyone might be equally poor but they'd be equally rich too. We have a massive economic capacity, largely misused to produce things of little value. We can provide for everyone. Capitalism creates no incentive to provide for everyone (as it serves capitalism well to have an underclass who will readily accept poor working conditions to survive), and market failures are frequent. Consider that public transit is much more efficient than everyone having a car, but that there is very little incentive to create good public transit systems under capitalism, not because they don't do their job well, but because they're difficult to run profitably.