"Theft" presumes that property was wrongfully acquired in the first place, hence nothing can ever be stolen if all ownership is wrongful to begin with. This would mean nature is always immoral.
By that logic I can go to a beaver's dam and systematically take all of his sticks - and it is morally justified? I can take all the sticks a beaver is using for his future or present family and dump them on a rival beavers dam. Under your OA this is the height of morality, impeccable behavior.
Property is only theft, because you may inherit it to your children. If your property ceased to exist the moment you die it would be ok. Right now you may own something you never worked for. Poverty/wealth are determined mainly by birth. Its like the divine right of kings. Not justifiable.
Private property is an aspect of a social formation which is not natural, involving the appropriation of the commons for private use. Humans have lived for hundreds of thousand of years without the enforcement of the modern concept of property.
sources:
It naturally follows that the appropriation of the commons, a commons previously available for use by all, is achieved by force, for no voluntary transaction could occur - those holding all things in common would have no private property to exchange.
Tracing the right of property back to its source, one infallibly arrives at usurpation. However, theft is only punished because it violates the right of property; but this right is itself nothing in origin but theft.