I don't think you appreciate just how much goes into physically and mentally preparing yourself to compete at the highest level and how much it takes to come down and recover from competing at said level. If you've ever dedicated much time to serious training you'll know that it's often recommended to give 36-48 hours between training sessions in order to recuperate properly to maximize your workouts. We're not just talking about muscle recover but also recovery of the neurotransmitters used in order to send the signals for your muscles to their jobs and you also need time to boost your hormone levels back up to a working degree.
Add in the fact that these guys are travelling (an added stressor) and usually don't sleep as well the day after a game (especially when travelling) you wind up with players who aren't getting the proper rest physically, mentally or emotionally.
Ask anyone involved in the game if teams play too much for optimal performance. It's absolutely the case. They can do it and they can get by for the most part but the performance is far from optimal. It's because of the compounding wear and tear these guys subject themselves too by playing so frequently without proper rest. There's a reason why you see elite NBA franchises like the San Antonio Spurs limiting the minutes and the number of games played for their players. They are interested in optimizing performance. They see the value in having fresher players and can do so because the professional ranks are burgeoning with high calibre athletes. A fresh sub is really better than a tired starter for a lot of minutes. It's where sports are headed.
Ok, somewhat convincing, but where do you draw the line then? If 120 minutes of game time in 2 days is too much, why isn't 60 minutes of game time in 1 day too much? Why not give your backup the 2nd period?