Why aren't corrector plates aligned with the center of curvature in an SCT? According to wikipedia, Schmidt corrector plates must be aligned with the center of curvature to eliminate the spherical aberration. However, in compact SCT designs by Celestron and Meade, that is clearly not the case since the optical tube is usually shorter than the radius of curvature of the primary mirror. My question here is WHY?
In a schmidt camera, the corrector is placed at the centre of curvature, which is at a distance of twice the focal length from the primary mirror, and minimizes aberrations such as coma and astigmatism.  This makes for relatively long telescopes, particularly with large primary mirrors.

The sct design is similar, in that it uses a corrector plate, but this (along with the secondary mirror) is placed slightly closer to the primary mirror than its focal length.  This design allows much more compact telescopes, but at the expense of more aberrations.  As with most if not all optical designs, it is a compromise.