I'm not interested in stopping teens from having sex. I'm interested in stopping teens from having bad sex. Which includes not only unpleasurable sex (although that is important, too), but risky sex as well.
The teens who don't have sex are, obviously, not having bad sex, and are therefore not part of the problem. Telling the teens who are having bad sex to stop having sex altogether isn't going to work. The only solution is to encourage teens to have good sex (which means safe and pleasurable sex), if they choose to have sex at all.
If more teens having sex is the cost of less teens having bad sex, I will happily pay that price. Unfortunately, more teens having bad sex is the cost of less teens having sex overall, and that is what most of the people invested in teen sex education seem to have as their goal.