I've worked a little with commercial eye tracking software. It's typically paired with an infrared sensitive camera and IR lighting because the pupil stands out more against the iris under IR light. It also benefits from a rectilinear camera lens and/or software calibrated lens distortion.

Environmental challenges like lighting conditions, glare, whether the user has glasses or hair obscuring their eyes need to be controlled. If the user is looking downwards towards the screen, their eye appears more closed making it hard to accurately find the iris location.

You also need an accurate measure of the position of the head/eyes relative to the camera. So dedicated hardware like a depth camera might be needed for high precision tracking. Depth cameras come with their own set of issues.

The resolution of even a high-res camera versus the change in pupil location for small eye movements means that by the time you crop out the eyes, you might only be working with a very small image (<100pixels or less). Even with subpixel hinting, there's not a lot of detail left. Small errors here and in the head tracking location can cause large errors in the screen position estimation.