I've always heard the reason for the 46 active day is to minimize the advantage of a team with a completely healthy roster vs a team with injuries. That works in the Saints' favor. You don't want to go against a team with 7 extra healthy bodies that they can rotate in while we're pulling up players from the streets just to field a team.
I don't think teams lose because someone's bottom roster is better. There is very little differene between 46-53 guys and P/S or street guys they are all still some of the best football players.
The bigger cause of losing in that Situation is that the loss of a big time Stat player was too much to overcome. No bottom roster guy Is going to cover for that.