Short answer: in-camera software isn't powerful enough to do the best quality CA-correction, and taking shortcuts could destroy data and make it impossible to do a better job later. So if shooting JPEG only, it depends on how much post processing you want to do. If shooting RAW, it doesn't matter what option you choose, and if shooting RAW+JPEG, turn it on.
Long answer: Chromatic aberration is very complex. It's not simply an issue of RGB channels being at different sizes, because real light does not come in discrete red, blue, and green wavelengths only. Complications:
A) Each type of color sensor in your camera actually records across a whole range of wavelengths, some of which may overlap with the other sensors' ranges, etc. etc. The result is that the RGB channels can be distorted in weird ways such that the same object might be different shapes in each channel.
B) Also, some information is lost forever by poor optics and may have to be "invented" in order to make the image look better. For one example, if chromatic aberration causes an object to entirely fall outside of the sensor in one channel but not the others. It wouldn't be recorded at all and would have to be extrapolated.
C) The 3-dimensional shape of the scene will affect amounts of CA, etc., and your camera doesn't know what the 3-dimensional structure of the scene is precisely.
D) The amount of CA often does not vary evenly across the lens. It will interact with spherical aberration, etc. in complicated ways.
E) Channels will be at different focus from each other, so one channel will usually be sharper than the others. Re-aligning them alone will not fix this, and there is no way to perfectly or objectively fix softness.
Correcting CA, therefore, can be very complex. Fixing these things requires powerful algorithms that use a large amount of processor power and may even require some amount of human decision-making to create the best possible end product. It would be impractical to do this type of highest quality processing in-camera. So if you want the best end product, it should done in post processing instead, and the camera shouldn't touch it at all.
This only applies to JPEGs, though. So if you're shooting JPEG only, you need to decide: "do I want to do more post processing and get a higher quality correction? Or do I not care about absolute pristine quality and would rather save time by using the simpler, rougher correction in camera?"
If shooting RAW only, it doesn't matter, because in-camera correction won't be applied to the image anyway, even if you have it turned on, and your converter software will do a better job.
If shooting RAW+JPEG, then turn on your in-camera correction. Because you would only ever use the jpegs themselves for previews or if you wanted a quick and dirty product, and quick and dirty CA-correction fits the bill. Or if you want the higher quality processing, you would be using your RAW, so there are no drawbacks.