It's just too easy to re-invent a particular bit of "IP". I mean, I've done some of those on-line "C Programming Interview Test Questions", and come up with something identical to the given answer, except for choice of variable names.
Independent invention just ruins "IP" as property.
Patents exclude independent invention. If we both invent the same thing and I have the patent, you cannot use your invention.
Trademarks allow independent creation in separate geographic areas, but a pre-existing use can exclude an independent creation.
This is one of the many reasons that "Intellectual Property" is a misnomer - the differences between copyrights and patents and trademarks are probably larger than the similarities.
I also agree with your reason for "IP" as a misnomer.
I wanted to speak in a general or philosophical sense. not in a legal, specific sense. The internally-inconsistent concept of "Intellectual Property" founders on the rock of independent invention, if you reason from first principles, rather than attempting to propagandize your way through to some kind of state-enforced monopoly.