The Creative Commons License is helpful if you create a work and want to allow others to use it. Works uploaded to the Werner Icking Music Archive, for example, are frequently posted with the Creative Commons License.
The problem with posting music to Contrebombarde Concert Hall isn't posting the score (in fact, CCH won't let you post the score--the PDF file type, or file types of common notation applications, is not allowed). The problem is posting a recording of a work. That's not an issue if you're posting a recording of a score that is not under copyright. The problem arises when you post a recording of a score that is copyrighted.
Copyright law in most countries (including the U.S., Canada, and the E.U.) includes something called "mechanical licensing". That covers the recording of a copyrighted work. When you distribute a recorded work, a portion of the proceeds is due to the original composer--each country has an organization that licenses works for recording, and makes sure the composer gets paid. In the UK, for example, that's the Mechanical Copyright Protection Society. In the U.S., for some reason, we have two: ASCAP (American Society of Composers, Artists, and Performers), and BMI (Broadcast Music Inc).
For the vast majority of work on CCH, there's no issue. But if you're making a recording of a copyrighted work, you have to license it from the composer (or the licensing organization in your country). If you don't, both you and CCH could potentially be asked to pay up.
How likely is that? Hey--we're not rock 'n roll. The very biggest hits on CCH have barely over 10,000 downloads. But record companies are actively scanning the Internet, looking for web sites that post MP3 files that may be in their catalog.
I recognize that many people will not be enthusiastic about having to go get permission--or worse, pay for a license--in order to post a file of your own performance. It's frustrating. But its how composers get paid. (And, for what it's worth, a lot of churches and other organizations DO pay an annual licensing fee to cover licensing for public performance of copyrighted works--which is an entirely different subject.)