The main reason is radial imbalance.
Think about the center of the axis of travel (the center of the former). The moving mass should ideally be balanced and equally distributed and suspended from the center axis, as in a traditional round woofer. This will give the most predictable linear performance from the driver. A square cone is not radially balanced and the surround will not exhibit perfectly even suspension characteristic especially at the corners of the square. The square surround/cone is makes linear excursion more difficult. The outside corner will have to stretch and the inside of the corner will have to compress much more. As much as Kicker has attempted to improve on this, it still represents a weak point where as in a circular surround the surround exhibits even movement all the way around. That is why EVEN SQUARE SUBS STILL USE ROUND SPIDERS. Likewise, the magnet, the former, the voice coil, etc. are all still round.
Another reason is that a round cone can maintain the same level of rigidity all the way around the cone due to the radial symmetry. With a square shape, it is more difficult to keep the entire surface evenly rigid. Although the Kicker cone is heavily braced and reinforced to prevent this, with a powerful motor anything will tend to flex even a little bit. The uneven flex of the square cone can lead to increased harmonic distortion. Along the same lines the square cone itself will experience more complex and less predictable breakup modes across the cone's surface, again due the the radial imbalance. This isn't really an issue in subwoofers, but it is an issue for square speakers in general.
More importantly, I have yet to hear a square sub sound as good as a round one.