There is a reason in both directions. The DX lens, as others have pointed out, is for an APS-sized sensor 23.7 x 15.7 mm much smaller than the 35mm film size of 24mm x 36mm. Since they are optimized for the small sensor, they may not even cover the larger frame and if they do, the quality in the corners may be severely compromised.
On the other hand, film lenses over the sensor may be compromised as well. To the best of my knowledge, the DX sensor is not highly reflective. However the sensor that Kodak used in their Nikon-based 14n was, and many of the Nikon lenses were disasterous when mounted on this camera. The rear element of some lensese is also reflective and it set up reflections bouncing back and forth, between sensor and rear of lens creating ghost images of anything bright within the image.
The basic nature of film and sensors are quite different. Film has sensitized layers one above the other that respond to the only certain frequency bands of colour. While there may be some fall-off in the corners with superwide lenses, film really does not care what angle light hits it.
Quite the opposite with sensors. They have minute photosites covered with filters sitting side by side as in a mosaic. They function best when light hits them perpendicularly. DX lenses are designed to do this, while film lens designers never needed to consider angle. Thus a film lens on a digital camera may perform magnificently or it may be a disaster or it may be just a bit less than optimum. It depends upon the individual lens itself when mounted on the specific camera.
Of course there are other considerations. Since the DX sensor only crops out the centre portion of the image, a 1.5x cropping factor comes into play. A 24mm superwide lens is in effect converted to just another 35mm wide angle lens (36mm actually). With most lenses, the centre of the image benefits from the highest resolving power of the lens, while it may fall off a bit toward the edges. With film lenses on digital cameras, the image comes from the "sweet spot".
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