I have had the same thought, except that statistics is also taught in a lousy way to prepare people who will do publishable research, which is almost nobody. I also have the separate concern that since we teach kids new math skills every year, we never have high expectations about their ability to apply them, leading to weak problem-solving skills.

Just have everybody take a class called "Math for Being Smart" in their senior year of high school. First half is solid word problems; second half is probability and statistics, only you learn how to think about it instead of how to do a t-test by rote. Require it for graduation, and pass people on the basis of a skills checkoff instead of test average.