It the bigger is better principle is extented to other fields, the difference comes into view. If larger IC features were a lot larger, it would handle more current but capacitance would prevent speed, and density so reading the forum would require a computer that would fill a stadium in size and pull more current than a mid sized town, and have top clock speed of megahertz instead of gigahertz. Or sport cars, where lighter cars can carry less tonnage than a heavy all terrain vehicle but can navigate a chicane hardly without lifting from the while generating much higher g-loading. An owner of one often has the other as well. There are advantages when matching needs of work performed with the tools most appropriate. A sports photographer wants speed, low light performance and durability. Image quality is met by a wide range of current cameras. Speed is helped by lower moving mass, a shutter and mirror assembly can be made faster if for DX proportions. Smaller lighter things often need less mass to be durable than heavy things which need more weight for any given construction technique to have the same resistance to most abuse. Drop a 40 megapixel Nokia phone on concrete from 5 feet and then drop a D4 from the same height. The odds are high that the D4 would suffer the most, while the cell phone would be expected to keep working exactly the same without concern. A 400mm 2.8 is a fantastic lens but a monster to attempt hand holding, it is also $14000. Mounted on a D7000 or D300 it has the field of view of a 600mm. On FX, the same animal, bird or play that fills the frame on DX would require a 600mm 2.8 which would weigh about what a small sedan would but 4 times the cost. So FX users, to get that sort of reach have to resort to very expensive lenses, more expensive supports, or use Teleconverters which impact image quality and light transmission more than the difference between a good DX sensor versus a similar technology FX sensor. Not everyone thinks FX is the answer.
The only area that a sports shooter(or wildlife photographer) where is better off with FX is noise at higher ISO. They pay more for a tougher build camera to get the more massive mirror to move fast, to support its own weight and pay much more for lenses which become less transportable. So both systems are used by most photographers who need IQ for some assignments and reach on others at the top priority. FX does not replace DX, it just extends a photographers capabilities by both. I have both and use both where there is an advantage for the needs of the shot. A pro type D400 in the line that is fast and with the great AF system of the D4 will not be cheap but it will be popular with sports and wildlife shooters. There is room for both a D7100 grade camera and a D400 at the $1300-1400 range for the former and $2200-2600 range for the latter. IQ would be about the same. Stan St Petersburg Russia