The problem with TKD and karate in HS is that you're likely to have an opponent that either wrestlers or plays football (or in my area, boxes). All of those are bad matchups for TMAs. And at least when I was in HS, wrestling was mandatory in gym class. Don't know if it still is.
I was around some dumb shit teenagers leave their HS the other day, and all the guys were double legging each other and what not. HS kids wrestle in the US; even if you're not on the team you wrestle with your friends who are.
And in my area, there is a huge tradition of boxing. One of the two year olds my son was playing with the other day was learning boxing from his dad, and I plan to do the same in time.