The optics were designed by an optical engineer that designs optics for Cannon Cameras. This is a 4 element / 2 lens design (fully CA corrected) with multi-asperic radii. This means that the correction for grid distortion is part of the precision optical design and does not require an additional lens.
"Multi aspheric radii" is just another way of asserting that cylindrical lenses are "aspheric". While their profile is indeed not spherical, but only circular in one direction, cylindrical lenses are not usually included in the "aspheric" class. If they were,, then simple prisms would be "aspheric" as well, as they are non-circular too (i.e. flat). Cylindrical lenses are only "aspheric" in an unrealistically pedantic sense of the word, and are not classed as such in mainstream optics.
True aspheric lenses conform to non-circular profiles: cubic, polynomial and parabolic forms being examples of these. A simple cylindrical lens is not aspheric within the meaning of the term as it is used in optical design.
Aspherics are typically diamond-point polished right down to the final finished stage on machines costing millions. For this reason, they are usually quite small, due to the cost of producing them. Accordingly, when used in cameras and the like they are usually one of the smallest elements, close to minimum aperture size.
A true aspheric lens of the size indicated in the photograph would cost a small fortune to manufacture. This would render the sale price of any large projection lens, in whose design they were included, absolutely prohibitive. Employing multiple
aspheric lenses of the size indicated would be complete overkill to the nth degree.
As to grid distortion, no simple 4-element anamorphic lens can correct for BOTH grid distortion AND retain focus to High Definition standards. This also applies to prism-based lenses. There are simply not enough degrees of design freedom in 4 elements to correct for color aberration, eliminate distortion, and keep the image sharp across the screen.
4 elements - in two groups of two elements - are the absolute minimum required for anamorphic projection. You can't do it with one lens, but you can with two. Adding more lens groups may provide extra degrees of freedom by which the designer can reduce other aberrations besides astigmatism and color aberration, namely grid distortion.
Adding extra lens groups is a common (indeed sometimes the only) way of enhancing the performance of an optical instrument. Extra glass is not usually added for fun, as doing so will inevitably increase the cost and complexity of manufacture, assembly and calibration. There are very few "miracle" short cuts in optical design, no matter how clever the designer.