>Only scarce things can be property.

Abundant things can be property too. Property is about ownership. Intellectual property is a subcategory of property. It isn't an oxymoron.

>NDA do not protect IPs.

But they do indicate intent.

>someone can "steal" (copy) my beatiful design

I was talking about the physical object. They may think it is of such importance that it should live in a museum instead of as your private property. Other people believe that a museum could preserve it better and they think they know how best the pendant should be used than its actual owner.