I saw this question submitted to an on-line Q&A and the answer was 'that it made it fairer for a game if one team had more injured players'. I think that's somewhat of a lame answer. For football, injuries are expected. The concussion protocol now makes it even more likely players will miss games.
I think it would help all teams a lot to add at least 5 more players to their rosters and have all available for a game. Look at the Bills right now. With the 53 man limit, they chose to keep 4 CBs and 4 safeties. With just about all teams running 4 and even 5 receiver sets at times, you need those 4 CBs all active. Still, if one or more goes out with injury, you're screwed. Gaines got injured so the Bills had to activate Mabin and drop a player at another position.
The NY Giants on Sunday had 4 WRs go out with injury, which of course is rare. They were forced to play multiple TEs and split out RBs. They probably would've lost the game anyways but those injuries made a win more difficult.