When you use CC-licensed content, time spent searching for a copyright owner to ask permission to reuse, remix, or share “All Rights Reserved” content is channeled to research, create new works, or teaching.
Different CC-licenses permit and/or limit specific uses. Here's an infographic to help explain what is permitted and required by each license (in context with public domain and standard "all rights reserved"). Licenses are organized top to bottom from most open to least: