my expert friend (and he won a MacArthur Genius award for this kind of thing) says that only symmetrical designs are easily fixed with RAW CA tool. Asymmetric not so good.
Hmm. I would have thought it was the other way round.
Lateral chromatic aberration causes the sort of colour fringing where each spot is imaged as a stubby spectrum, always orientated radially from the centre of the image. There is basically a slight magnification difference as a function of wavelength, and it can be corrected to first order by re-dimensioning the Red and Blue channels to coincide spatially with the Green. This is easily done in digital post processing and there is a proper optical basis for doing it: each of the RGB channels contained a pretty sharp image; they were just out of register with each other.
Axial chromatic aberration, or secondary spectrum, is a lot messier. It does not vary with field position, only with f-number - it's the type that is worst at wide apertures - and axial distance from the plane of focus. Only one (usually) of the RGB channels contains a sharp image; the others are out of focus. There is no rigorous optical basis to post-processing algorithms for correcting this - from what I've seen, they seem to work by cosmetic fudges like desaturating the fringe colour, rather than by physics - although, from Doug's attachments, it's clear that some of the fudges are more successful than others. At the plane of focus for one colour, you cannot push the other defocused light/colours back into focus, post-capture. The closest you can come is with some sort of adaptive, channel-selective deconvolution process. But that is non-linear, unpredictable, locally variable, and stuff like the noise statistics then go out the window. Outside the plane of focus, where the axial chromatic is manifested as colour fringing on the bokeh 'blobs', even deconvolution alone won't work, because there is also a spatial offset between the defocused fringes of difference colours. That sounds somewhat like lateral chromatic, but it doesn't have its global invariance; rather, this effect varies locally with each bokeh point. To truly correct it would require knowledge of the degree of defocus of all points in the image. Talk about messy!
So what about the lens design? Symmetrical lenses exhibit minimal lateral chromatic aberration, by virtue of their symmetry. Since they lack the easily correctable type of fringing, I don't understand why they would be more "easily fixed with RAW CA tool" than asymmetric lenses, which can show both types of aberration, including dollops of the more easily correctable type.
PS. Do I now qualify for a MacArthur Genius award?