Maybe I am not following. It seems like a way to get around a rule.
Chaim'ke, my dear, sweet Chaimke. The eiruv does not permit one to carry where it is Biblically prohibited to do so.
The Sages EXPANDED the Biblical prohibition of carrying to apply not only to a true public domain but also to places that even
appear like a public domain. (A public domain as defined Biblically would be like Times Square. A place that appears like a public domain would be like the block where you live.)
The Sages created the eiruv to permit one to carry only in those places that merely
appear like a public domain. Guess how? But making it no longer appear like a public domain!