I'd never travel with the camera inside a mechanically operated housing because a bump to one of the controls might damage the camera. It could break a button on the camera itself or crack the touch screen. Electronic controls don't have this problem, although my experience is that electronics have other problems
On the other hand, as you point out, putting the housing inside a carry-on may cause it to be overweight and oversize. Gates housings are tough enough, and can be padded inside the checked bag with a wetsuit.
Maybe the future will bring 8K videocameras with superb white balance etc. that are smaller than the GoPro including the housing