Copyright has a limited relevance to science. It applies only to copyrightable information that includes working and peer-reviewed papers, books and articles, and presentations, videos, photos, and other such creative works. The weakness of a copyright-focused CC are:1
There are many other works involving other forms of IP and legal arrangements such as patents and specifically contracts such as material transfer agreements (MTAs), data use agreements (DUAs), informed consent, terms of services (TOS), etc. that are very important in science.
And, generally copyright does not apply to data as they are considered facts without sufficient creativity. In some cases, other rights might exist in data, but those rights are have traditionally not been covered by copyright licenses such as CC licenses until very recently.
The narrow focus of Creative Commons has arguably contributed to its success. By focusing on copyright, Creative Commons has ensured a widely scalable solution via its licenses. Similarly, by focusing on “open” to mean “free to access and reuse with no more restrictions than prescribed by the license,” Creative Commons licenses offer complete and unrestricted reproducibility and reusability. For example, if I create a work and offer it under a CC BY license, anyone can take and reproduce it without asking anyone for permission from me. Not just that, anyone else can take that word from the first present from me without asking any for the permission from me. This unrestricted ability to copy and reproduce the work has led to an unparalleled adoption of the licenses, and possibly the reuse of CC-licensed works, worldwide.
There are also properties inherent to copyright that make it easier to add copyrightable works to the commons. Copyright springs into existence naturally and immediately upon creation of a work, and doesn't require an imprimatur from any authority. A bottle of olive oil can't be labelled organic unless vetted by a suitable certifying authority. An ISO mark can't be applied unless earned. But not so with a copyright license. This makes it very easy to apply copyright licenses thereby growing the commons. However, it is entirely possible the license may have been applied wrongly, that is, to content that may not be copyrightable. There is no guard against this except using the work in breach of the license and defending one’s use. Additionally, this ease of applying a copyright license also makes the commons susceptible to misinterpretation as was evident by the collective heartburn caused by the recent Flickr brouhaha.
Attribution, provided via citation, is the main currency in science. Citation is converted to recognition and rewards such as promotion and funding. The mandatory attribution requirement in all CC licenses is a good thing for science, but science was doing this all along. One could argue that sensitizing academics about the legality of sharing has muddied the waters by impinging on their limited bandwidth with considerations extraneous to their science. Scientists now have to make an explicit decision about their work. Given the irrevocable nature of CC-licenses, scientists now think twice before applying a license on the very work that, until they learned about copyright, they were freely sharing with other colleagues, even with the general public.