We humans are sensitive to every tiny detail of the eye, because we express so much emotion through it. It's no joke that the "eye is the window to the soul". Gaze correction software literally winds up looking like it messes with your soul.
Maybe someday we'll invent gaze correction that actually looks realistic -- but because it involves not just moving the eyeball, but opening/closing the eyelid (the eyelid moves as our eyes move vertically, like for a webcam), therefore moving the eyelashes, involving compensation with the lower eyelid, and more... it's going to be really hard.
With a depth camera you can move the camera's entire vantage point as if it were behind the right area on screen. Hat's probably a better approach, along with AI filling in the disocclusions (more cameras can also do this).
https://appleinsider.com/articles/20/06/22/facetime-eye-cont...