Well, the solution to other systems seems to be "it's checked in, therefore it can never be un-checked-in, so deal with it!" (or at least this is the attitude of some vocal proponents of them).
While I'm certain you and your organization have a perfect record of never checking inappropriate things into your git repository, mine does not. Even if all the employees at your company were perfect, there is still a chance of inappropriate information getting into the repository.
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The inability to, in any remotely easy way, remove mistakenly checked in large files and private data has always seemed like a major flaw with git.
Well, the solution to other systems seems to be "it's checked in, therefore it can never be un-checked-in, so deal with it!" (or at least this is the attitude of some vocal proponents of them).
The flaw is in having this "private" data in a public repo to begin with. If your data are private, don't put your project on github.
While I'm certain you and your organization have a perfect record of never checking inappropriate things into your git repository, mine does not. Even if all the employees at your company were perfect, there is still a chance of inappropriate information getting into the repository.