Please point to some examples of bad calls that were made because the referees were out of position because they were unable to keep up with the athletes on the field. I mean, I can think of plenty of bad calls but I am not seeing an overwhelming number of them arise because the referee was too out of shape to be in the proper position.
Take, for example, the horrible pass interference call on Asante Samuel against Denver last year. Or the Carolina-Chicago out-of-bounds call (reversed by replay). Or the Ben Roethlisberger TD in the Super Bowl. In every instance, the ref was in the proper position but made the wrong call. How is a workout regiment in July going to solve that problem...?
Weekend warriors or not, the mechanics of NFL officials are the best in any major sport, pro or college, except for MLB.
The game has gotten faster and way more complex and that makes officiating harder, but not because these guys are out of shape or out of position. It's because it's way more difficult to anticipate what's going to happen on the field. A good offense has 200 plays and a good defense runs dozens of different looks during a game. These are finely tuned plays that are possible in the video era of multiple cameras with athletes who are faster and stronger. As the emphasis in the NFL moves toward coaching -- trying to keep the offense and defense confused -- the result is that very same thing happens to officials. Just like the teams, they have no idea what the call is going to be. A baseball umpire knows that within his jurisdiction, there are like 5 things that might happen, and he sees each of them 75 times a week. A football umpire or ref in the playoffs sees something he's never seen before almost each play.
If you throw in the fact that the league has made literally dozens of complicated clock changes in the last few years to get in more commercials, and has tinkered with passer protection and pass interference incessantly, and you've got officials with an awful lot on their plate. Just think about what the average ref has to do on every play. 5:10 left in the 4th quarter, player runs out of bounds, line up at scrimmage and quick snap, false start. Wind the clock or not after the reset? Well you only know if you're paying attention to the time, understand the 5:00 rule, understand the new rules about clock stoppages depending on whether the clock was stopped at the conclusion of the last play (it was not, the 25 second clock rewinds on OOB with 5:10 left), etc.
Imagine everything that the line judge has going through his head on a blocked field goal, for example. Whether the ball goes past the line of scrimmage (where the line of scrimmage even is), who touched it first, where the play ends up. While everyone else is already staring at the uprights, this guy is looking for neutral zone infractions, substitutions, procedure, and then also having to anticipate the play that happens only twice a year.
Officiating in the NFL is freaking hard. It's a constant balet where you need eyes in the back of your head and you have to be aware of everything going on around you.
