1. Ensuring that the creators are compensated based upon the perceived value of the work, as determined by the market.
2. Ensuring that everyone in the chain of creating the work is compensated. This includes authors, editors, typesetters, marketers, etc..
3. Restricting access to a work. Certain publications are intended for limited audiences, and copyright is one means of doing so.

Yes, a lot of that has to do with compensating the creators and thus ensuring their contributions. But it is important since other mechanisms of encouraging the development of new works is controversial and often ineffective. Consider something like government arts funding. Many people are opposed to it because they don't see the value of the work. In a lot of cases it is because that work either has no value or has value to a very limited audience. Market forces diminish that argument because a work that succeeds in the marketplace must have value to the people who are willing to pay for it.

I would also argue that copyright offers fewer restrictions by imposing more restrictions. In a copyright model, it is possible for creators to offer their work under less restrictive licenses (e.g. FLOSS and Creative Commons). In most countries it is possible for creators to place their work into the public domain. And yes, it is possible for creators to work within the confines of the traditional copyright based business models.