The general consensus among fans and strength coaches is that football players are elite athletes mainly because they play on a high level. To a certain extent this is true because on a professional level there is no higher level. On the collegiate level the top Division I schools are considered to have the best athletes.
However I disagree with this consensus because most of the players can be improved greatly. All athletes, regardless of level can be made better. However, the amount of improvement on the highest levels is usually quite small. When we see many players who can be improved a great deal, it indicates that they are not on the highest levels possible. Thus they are not elite.
There is another and possibly the most important, reason why football players are not elite athletes. It is because they can see great improvement in their performance from doing general strength and conditioning exercises. A truly elite athlete has a very narrow range of exercises that he can do and the exercises are for the most part, all specialized.
This means that the exercises duplicate a portion of the technique together with the strength or other physical quality being developed. In other words, when the athlete performs the exercise he develops the muscles in exactly the same way as they are used in execution of the game skills. However, the number of exercises that can do this is relatively small.
If an elite athlete did many general exercises instead of seeing improvement in his performance, he would see poorer execution — except if he were on a sufficiently low level. Thus when you read about an athlete and his training program and how he improved from doing general strength and/or explosive exercises it immediately tells you that there is great room for improvement and that he is not elite.
Football has evolved greatly in a last few decades but only partially because of better skill and play abilities. Anthropometric measures such as bodybuild, height, weight, arm length, etc. have been responsible for most of the player improvement. The game itself has evolved many because of changes in strategy and especially in different offenses and defenses.
However, football still lags greatly behind other sports where it is possible to find truly elite athletes. But because skill execution ranks very low on a priority list for football coaches, do not expect to see major changes in this area. If more attention was given to skill execution and specialized exercises I believe we could see the game of football taken to a much higher level.
For more information on the differences between generalized and specialized exercises see Build a Better Athlete. The differences are also spelled out in some of the specialized explosive training books.