Ok, so i read that Library of Babel thing... Not sure how it's relevant to protecting copyright.
Because you don't want to see. How many books are in The Library of Babel? How much effort does it take to find a book in the library that is actually meaningful, literary, coherent, complete, etc? What is the value of that search? You can think of that interesting book (as well as all the ones that are not interesting) as a unique number. Does that number exist independent of its discovery? It does, but in the same sense as a nugget of gold buried deep in the ground. Naturally, there are permutations of some particular number, but we'll leave that to the mathematicians to decide what constitutes a largely similar work. Moby Dick with a few misspelled words and a deleted paragraph or two is still Moby Dick.
When you copy a number, it's not really a copy, as you believe it is. For example, 3,453,232,343 copied results in 3,453,232,343. According to mathematical theory, it's the same entity. There really is only one 3,453,232,343. While the number used as an example here is too small to warrant copyrighting, the size of a number representing a book or a film does, due to the fact that it can be mathematically proven that it is statistically unlikely (impossible for all practical purposes) that any other human being ever born would ever discover it, or produce it again.
A filmmaker or an author is really just someone exploring that space within The Library of Babel. The space is so huge, there's enough to go around for everyone. The resources so vast, it makes the resources of our planet, even the Universe appear minuscule by comparison. Therefore, if you argue for ownership of physical property (something which is very limited in extent), then it is rather hypocritical to deny the value that should be accorded to those who discover or produce a meaningful number.
In summary: to copy a very large number is to steal it, because the notion of copying a number is meaningless mathematically. Owning a DVD which contains the number is only ownership of the plastic DVD, not the number.
If you wish to think of it as homesteading, then by all means, think of it that way. This is what renders all small numbers generally uncopyrightable - say numbers less than 2^1000.