I definitely feel that some general, at least survey-like philosophy courses should be taught at the high school level.
Thinking philosophically can be a fun and useful skill to have. When I was younger, I thought I was interested in philosophy, but my interests in it quickly fell by the wayside because they weren't nurtured in school. I kind of feel like that is a shame.
Somewhat specifically, I find that philosophical thought and a knowledge of the history of philosophical thought can be particularly useful in regards to political thought, something I think all citizens should do at least some of. To be blunt, I feel that a lot of Americans are politically ignorant, and this can be attributed in part to the fact that they haven't been properly acquainted with philosophical thinking.
I'm reminded of the proverb "Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime."
Instead of just giving them knowledge, which is useful, but most of which they will forget, we could also give them the ability to think and learn for themselves, which is a skill that they can benefit from throughout their lifetime.
Do you think many Americans would have concerns about high school philosophy classes possibly fostering atheism or agnosticism in children, and therefore oppose it? I mean so many people have a problem with evolution being taught in school, I have to wonder.