hm, tricksy one. I can understand why a music school might not teach historical flutes in sufficient practical detail for one of their students to feel confident to teach or play them in later life. The flute was in a constant state of evolution over a long period from which we draw music we enjoy today, so it would be hard to know which instruments to pick and teach. Lisa Beznosiuk (lead flutist of the orchestra of the age of enlightenment) has a lot of interesting YouTube videos on the different flutes she uses for authentic performance of music from different eras. To my mind, only a small number of flutists would have either the financial resources, or the skill/time to cover these aspects of historical performance as thoroughly as she does.
Meanwhile the other common wooden flute today would be the Irish flute, which again is different to the Baroque flute from which it evolved (it's louder, with bigger tone holes, but I believe this means its cross-fingerings don't work so well, so it is always played in restricted keys. This isn't a problem for traditional Irish music which derives its beauty from simple tunefulness, and doesn't require clever chromatic stuff. Almost everything is in D or G, and if it isn't, the Penny Whistle players will be seriously upset anyway).