I’d like to turn my head in. For a new one.
I think when, early on, people gave advice to turn the head joint in, they did so to communicate the concept of blowing down into the hole rather than across it. Turning it in changed the angle, and that alone facilitated the sound they aimed for.
But, their intent wasn’t so much to require turning the headjoint IN, but to show you easily how to get the sound they advocated. Once you had seen how to get it, then you would continue to get it no matter how your flute was adjusted.
Focusing on “turned in or turned out” seems–to me, at least–to be a misguided focus. It’s not whether it’s turned in, straight on, or out that matters. It’s what sound you are getting.
It’s not the turning-in that gets the sound–it’s the position of your head relative to the instrument. Whether it’s turned in or out, you can get the same sound by adjusting your head. It’s just more uncomfortable in some positions.
Get the sound first, then adjust the flute so that getting it is comfortable and so that the position facilitates getting the sound.
Note that I am no expert, so take the above comments at your own risk.