Recently I was looking for Nikon supertele lenses (500mm F/4 or 600mm F/4) and I recognized that they are all fullframe and really heavy lenses. Some of the newer lenses are a lighter than the older ones but they are still heavy. I know a few people who shoot those lenses on APS-C sensor sized cameras (DX) anyways to get "more reach" out of them. I wondered why there are no APC-S supertele lenses. I guess they could be a lot lighter and also smaller. Is there a good reason why such lenses dont exist? (I dont know of lenses from other brands - maybe Nikon is behind?)
Because making these lenses for APS-C sensors won't make them significantly smaller. The focal length and max aperture are the main criteria for the diameter of the front lens, that itself drives the size and weight of the lens. So you would have two lens line-ups (FF and APS-C), and given the smaller market for each the lenses could be more expensive than lenses sold for both.
On the other hand you can consider that the APS-C supertele lens exist, it is just a lens with shorter length. The APS-C version of a 600mm-f/4 is just the 400mm-f/4...
For shorter lenses (standard and wide angle) the smaller image circle is easier to take advantage of, and the market is big enough to warrant designing lenses specific to APS-C.
As focal length increases the size/weight/cost benefit of a smaller image circle becomes less and less. The required diameter of the front element needed to provide a larger entrance pupil, also known as the effective aperture, begins to dominate well before the "super telephoto" threshold of greater than 300mm is reached. Even a 400mm f/5.6 lens requires a 72mm entrance pupil, which generally means an 80mm or so front element. Likewise, a 300mm f/4 lens requires a 75mm entrance pupil. The front elements of long telephoto lenses tend to be about 10% larger in diameter than the rated size of their maximum aperture.
Most of the size, weight, and cost savings for lenses that cast smaller image circles occurs at the rear of the lens. With a shorter focal length lens that provides a wider angle of view the rear group is a much higher percentage of the total size/weight/cost than with a lens that provides a narrow angle of view.
In terms of cost, the most expensive element - made from higher quality low dispersion glass and usually aspherical - in most budget level telephoto prime lenses is either the rear element of the front group or the corrector element that is usually at the front of the rear group. Many mid to high end telephoto lenses use exotic glass for both of those elements as well as several others. So there's not much cost savings to be had by making the rear group slightly smaller with a long focal length lens. The front of the lens where most of the expensive lens material is located, because the front elements are so much larger than the rear elements, can't be any smaller for an APS-C lens than for a FF lens.
Just an opinion, but the APS lenses are typically less expensive and popularity seems for that reason. Telephoto principles make long lenses shorter, but focal length makes f/2.8 much larger diameter glass (regardless if DX or FX). So long lenses are expensive, which is likely of continued interest to owners of more expensive cameras. Same with macro lenses (except the 40mm DX lens). So I imagine the decisions are mostly about the prediction of which will sell better. The FX lens can be used on DX if you want it.