It's rather short-sighted to reply that "DX lenses are not supposed to be in existence".
Here's a summary of what I understood from "DX" lens design:
In the past, lenses were designed based on film. With the advent of digital sensors as light capturing devices, there might be some problems with conventional lens design. Characteristic of a lens may change when you change from a 1.5x digital body to a full frame digital body. For example, if some bright point of light is at the corner of the image then it might appear more than once. This is because light bounces between the low-pass filter of the sensor and the rear element of the lens then back again. This phenomenon is also known as ghosting.
A vintage Nikkor lens might give excellent result on a film camera but not on a digital body. This is not because the lens is below par but it wasn't designed with the digital sensor in mind. Light can hit film from a wide range of angles, and as long as it's properly focused, the film will record a sharp image. In digital sensors, light need to strike as close as possible to 90 degrees or the resulting image can display chromatic aberrations or vignetting. The problem will be much more severe close to the edges of a full-frame digital SLR, but still can be a problem even on those with "cropped" sensor. With an older or cheaper lens, the image defect will get even more severe. Nikon's decision to stick to cropped-sensor DSLRs makes sense since the imaging circle is smaller. Therefore, the edges of the 35mm-format frame will not be shown. The logical design of Nikon's "DX" lenses is based strongly on this reasoning.
Based on the reasoning that photosensors require the minimization of extraneous light and the adoption of the telecentric principle, lenes were designed such that the emergent rays from a lens arrive more vertically at the sensor across its whole surface. In this way, the microlenses which are in front of the picture elements receive the light on the optical axes, giving minimum aberrations and vignetting. Also, any reflections from the sensor's polished surface return vertically and thus can be optimally minimized from the recomputed coating of the rear lens element's surfaces.