I see two problems with this.
1. High school students are high school students, and only the top two (or three at max) actually get lessons and play tennis competitively. The rest are learners or casual players. Thus, they don't have the physical stamina to play singles and then doubles.
2. Many schools have a challenge system, where they play someone higher on the ladder and when they beat the higher seed, the two switch spots. One match can decide everything. If someone has an off day, and they lose, say goodbye to varsity and playing for the team. The point of having 12 players instead of six is to get more people playing tennis, too.
I really think number 1 is the real reason, but the college system just can't work in high school.
I am an unpredictable player. Even I surprise myself with some of the shots I make.