There's an important piece of background to understand why computational methods cannot completely correct chromatic aberration.
A photon can be any color of the rainbow. The reason ink and TVs can get away with using only 3 colors is because our eyes only have 3 types of receptors (cone cells). Each receptor responds to a range of wavelengths. "In-between" wavelengths will trigger multiple receptors. For example, a TV can send a mix of red and green photons and create the same brain signals as yellow photons would. Animals with more types of receptors, such as bees or the mantis shrimp, wouldn't be fooled by a TV with only three base colors.
A camera's sensor performs the same lossy compression as our eyes. Light comes into the camera in a range of wavelengths, and triggers each type of pixel a different amount. Each type of pixel has a sensitivity curve engineered to resemble the sensitivity curve of one of the cone cells in our eyes.
Understanding that natural light isn't just red, green, and blue makes it clear why chromatic aberration can't be fixed computionally. A green pixel can't know when it's receiving green photons that are perfectly aligned, or yellow light that needs to be destorted.
P.S. There cameras that can "see" a greater range of colors. Search for "spectral cameras" and "infra-red goggles"
PPS This is also why a RGB light strip might look white, but objects illuminated by it might look odd. You might be familiar with the fact that a blue object illuminated by a red light will look black. For the same reason, it's possible for a yellow object to be eliminated by red, green, and blue light and still look black.
PPPS This is also why custom wall paints are a mixture of more than three colors. Two paints may look completely the same, but objects illuminated by the light bounced off the walls look completely different.
PPPPS This is also why high-CRI lightbulbs are a thing. If you get something hot, like the sun or a tungsten filament, it will release photons with a wide range of wavelengths. Neon tubes and LEDs emit a single wavelength, so they must be coated with phosphors that fluoresce — emit light at a different wavelength than they absorbed. Using more kinds of phosphors is more expensive, but makes it more likely that whatever object is illuminated gets all the wavelengths it is able to reflect.
