It seems like the 8-16 limit is just as arbitrary as the 7-18 limit already in the rules (before modifiers).
Why is it that a score of 7 is min/max'ed while a score of 8 is not?
I don't think there is a problem with the score limit. The problem actually seems to be with the player's weak character concept (apparently), or your perception that they are somehow gaming the system.