I don't think the answer is having GitHub do anything about it. The word has to be spread, yes. But not that way.
Developers need to know about the importance of all their files and their security at development, else just think of what will happen when GitHub is not around or when they use another form of Git, etc. Problems need to be solved from the root and that means teaching developers to be more security aware, not making tools that will make said awareness easier to forget.