This isn't a good experiment unless the people involved have no knowledge of the child's birth sex.

Sure. This is far from perfect.

Also, as far as I'm aware, there's about one prominent case study describing this, and as such I think it's misleading that you use the word "frequently".

I presume that you are thinking of the David Reimer case. While that is the most prominent example it is not the only one. In fact, that case is actually is one of the less useful examples since there were many complicating factors. But there are a variety of other case studies. See, e.g. here.