Well Nikon has a GPS module (Nikon GP-1, https://en.wikipedia.org/wiki/Nikon_GP-1) for the hotshoe that does work, so I dont think that is the issue. Also at least on my D850, turning off the camera does not turn off the bluetooth automatically, and it can sync photos to the smartphone while the camera is off, so depending on how much power GPS would use, it could be possible to have it run in the background. And turning it off keeps some things running anyway, like showing the number of photos still available, so coordinates could be saved for a little while after turning off.
I had a GP-1 at one point. It would take several seconds to get a GPS lock, so about a third of the time my images had no GPS or I had to wait for the light to indicate it was working. Not very practical in my case. Also it connected via an awkward cable.