Stephan, you're still attached to the notion of an idea or intellectual work as a supernatural object, a universal all pervasive pattern. There is no such thing.
There is an intellectual work that exists in a person's mind, and may be set down by that person in a physical medium. This is a discrete object. It has no natural effect beyond its physically localised fixation. Because it is discrete, it can be owned and possessed, the information as much as the matter.
The ownership of intellectual work, its nature as property, needs no government to allocate rights over. It is the property of the person who creates or discovers it, for they can naturally exclude others from access to it. If I write a poem I can naturally exclude you from access to it. I can prevent you copying it.
You'll no doubt then say that I can't supernaturally prevent you writing an indistinguishably similar poem. And I'll agree, but then, unlike you, I don't recognise the concept of supernatural, universally pervasive objects, and the notion of allocating ownership over them (or not).
Obviously, once I've given you access to my IP, I can't prevent you copying it, but we can still prevent others copying what is now exclusive to us.
Ideas are scarce, limited by the scarcity of human beings to originate them. The fact that one can copy those ideas without limit does not make the ideas non-scarce. The fact that you can produce a trillion copies of the works of Shakespeare for a few pennies does not make Shakespeare's works non-scarce. The non-scarcity of digital copies is a red herring when it comes to understanding intellectual property.
Incidentally, one does not lose one's right to liberty, even as another's guest - one always retains one's freedom of movement and speech. Your natural right to privacy does not give you the power to subject your fellow man to your will within it, only to eject them from your privacy. Thus you cannot gag a guest, but you may eject them if you do not like what they say.
"Stephan, you're still attached to the notion of an idea or intellectual work as a supernatural object, a universal all pervasive pattern. There is no such thing."
Then what is it? What is the number 4 or the color red, if not a universal all-pervasive pattern?
"Ideas are scarce, limited by the scarcity of human beings to originate them. The fact that one can copy those ideas without limit does not make the ideas non-scarce."
Well, yes, it does make them non-scarce, if you stick to the definition of scarcity that most of us use. If you substitute your own definitions, you can claim whatever you want, but you'll have a hard time participating in a sensible discussion.
The only way to know how much profit someone "should" make is to see what people are willing to pay them for. Part of the market is the need to incur costs of exclusion. If you don't put a lock on your business, people will steal it. If drive in movie theaters didn't incur the cost of putting little speakers for each car, then people would free ride by watching it from outside. To decide whether a given endeavor is worthwhile, one must take all costs into account, including costs of exclusion.
The first sentence in bold is a false premise, and the second a red herring. Things like the free rider problem and exclusion costs introduce inaccuracies in the price measured by the free market. Because of these inaccuracies, some "endeavours" are undertaken while they are not socially worthwhile and some are not undertaken though they are. Removing exclusions costs makes the price measured in the market more accurate, not less.
The problem with copyright is not that it removes exclusion costs. That would be a good thing, increasing the accuracy of the price measured by the market, and thus making some worthwhile endeavours be engaged in that with the distortion of exclusion costs might not be.
Copyright, rather than removing exclusion costs, is in the business of removing monopoly costs -- the costs of maintaining monopoly. It does not prevent a non-customer from free-riding on your intellectual property. It prevents customers of your intellectual property from making copies and redistributing them. Copyright prevents a customer of your intellectual property from entering into competition with you.
Restricting competition is generally considered a bad thing. The only reason we accept a state-granted monopoly for authors and inventors is that we are afraid that without it, they would not author or invent enough. Evidence that this fear is a reasonable one is sparse. In any case, it is hard to objectively measure (on the market or otherwise).