I think you need to think in terms of the first derivative, which is the amount of training that the players get each minute. We know that the derivative is zero for m > 48. And the integral of the derivative for m = 0 to 48 is 1.0.
A huge drop in effectiveness below 48 also means that the minutes just below 48 are super productive. If you hypothesize that a player only gets 50% training for say 40 minutes. That means the minutes from 0-40 give just as much benefit as those from 40-48, or that those last 8 minutes are 5 times as effective as the each of the first 40, and then there is a complete stop. If this were the case, it would be no mistake that the coach is called a "trainer", because it would mean they were giving the players injections of training.
And why would they do that? It is virtually impossible to get 48 minutes for 3 players. And if there is a big drop, you are risking losing a huge chunk of training to a player who gets injured for the remainder of a game, or who is in foul trouble. So you would be better to make sure 2 players get 48+, but then the remaining time (20 or so minutes) would be essentially wasted. So you are back to a HT training system where you can train two players per week per position period, but with a lot of useless minute elaboration.
Instead if the training below 48 was something like (m/48)^2, there would still be a small penalty for coming up short, which would be enough to discourage someone training 4 players with all coming up short.
For example with 4 players each getting 36 minutes, they would get 0.56 training or a total of 2.25.
But 2 players with 60 and one with 24 would get 2.00 + 0.25 for the same amount, and the closer you could get the 3rd player to 48, the closer to 3 units of training.
60 + 42 + 42 would give you 2.53 units. So there is still an opportunity for much improvement, but without the need for a crippling penalty that some have suggested.