Strictly speaking, putting a label on classified information does not protect it. In fact, the appearance of protection may be one part of the problem–unless the label and the efficacious protection were to go together. As a theoretical construct, such a system looks doable.
Make the container match the level of classification. Labels with different colors do not actually protect anything. The strength of the container should be consonant with the level of classification of the information inside, and it could have other important features such as tracking who saw it, where it was, when it was viewed, etc.
In the case of paper, instead of merely having a file on a desk, one could have a file that is a container which offers protection and also records metadata. It might look like a file, but it is more secure: papers won’t fall out, the location of the file could be tracked easily.
Containers could be physical or electronic, and one could make them work together.