"I anticipate all sorts of crazy digital-rights management battles ahead for 3D objects like this - including art."
A 3D scan of an existing object does not create a new copyrighted work under US law. See Meshwerks vs. Toyota. This follows Bridgeman vs. Corel (2D photos don't create a new copyrighted work), which follows the famous Supreme Court decision Feist vs. Rural Telephone (which allowed loading phone directories into databases.).