As Marc noted, this is due to lighting. Unfortunately with sports we don't generally get to choose locations/poses and sometimes the lighting just sucks. On a football field, when you have strong downward angled lighting behind the player and a fair but lesser amount of front or side illumination, you get the effect you see in your foggy photo. Here are a couple of examples with the EF 24-70 f2.8 lens post game, both the same night, same field, post-game celebration but very different lighting where the players are strongly back illuminated and the second where the players are closer to the endzone and not directly backlit.
I have captured similar game photos with my EF 70-200 f2.8 IS III and no lens is going to make a difference, my favorite EF 400 f2.8 IS II will do the same under those conditions. You can improve things in post but nothing will totally get away from the issue, basically when lighting conditions really suck then that is going to have a major impact on the final image. I know for the fields I shoot where the problems occur and I try to avoid the problem angles at those positions but it isn't always possible.
Both photos with 1DX II and EF 24-70 f2.8 with very different results, the difference is in the lighting intensity and location. The washed out photo has already been heavily corrected for contrast in post, the original file is worse than your "bad lens" example.
Rodger
