This is a really interesting subject. As a musician, I have found that my most inspired moments seem to come from what I can only describe as a "higher place" outside of my regular consciousness. I know that this is a common experience across many different creative disciplines. It's as if you are channelling the creation, so it is really a gift that comes through you rather than something that exclusively belongs to you.
If this is the case, then the only reasons to exert intellectual property rights over the creation would be to satisfy your own ego or in order to monetise it to survive in this capitalist system where money is the only accepted and respected form of value.