Copyright is a red herring - it exists (in the US specifically, and generally, internationally) to protect creative/artistic expression. Short phrases (such as titles of books/songs/movies/etc) cannot be copyrighted, nor can bare facts (e.g., "The Washington Senators won the last game in the World Series by a score of 5-4".)
Further, there are a number of "fair use" exceptions which allow limited use of copyrighted works without the copyright holder's permission.
Trade secret is also not a great match - it protects confidential information/processes used in the conduct of a trade or business which confer a competitive advantage. It's not at all clear to me that the average person using BTC as a medium of exchange is engaged in a trade or business (they might be - but if I buy a cup of coffee, for my own consumption, with BTC, that doesn't sound to me like I'm engaged in a business) or that the use of a particular private key or keypair confers a competitive advantage.
I am not saying there are no property rights in BTC, but I don't think they're going to come from copyright or trade secret.
I do realize that I'm doing an experiment in idealism in trying to apply intellectual property law to Bitcoin. There are enough small counter arguments that I still find it interesting. But your point is well taken.
The Uniform Commercial Code explicitly defines General Intangibles as a form of property. If a judge is willing to allow that Bitcoin is simply a General Intangible, then it's future is bright. So far I don't see any other legal basis for property rights for Bitcoin until virtual property and virtual resource ownership are tested in court. Which they might have been and I just haven't found examples.
However, I do believe the block chain is a large distributed creative work. I also think its a problem that no license applies to the block chain as its copied all over the world. Very few people in the developer thread seemed to care. There is only one registered copyright with the word Bitcoin in the U.S. right now and its by CBS for "The Good Wife S3E13: Bitcoin For Dummies".
Bitcoins are nothing more than copied data that is processed by individuals collectively making their own contributions of data. "I own Bitcoins and I can spend them" is nothing but an idea. I believe it is an expressible idea, that the expression is creative, and that the mechanics involved in Bitcoin can enjoy protection under existing copyright law if all else fails.