It's a cool idea, and I know some teams have already embraced it. I've seen everything from making FRC an elective all the way through 1717's program of making it the senior capstone. I recall one of our local private schools has a fantastic team (1218), and something like 40%? of all students who elect to attend at least partially attribute their interest to the FIRST program, which runs (J?)FLL-FRC. Realistically, it'd probably be difficult to systemically bring FIRST into public school systems, but there are some success stories.
To be fair though, I'm not sure the average "When am I going to use this?" student would take "well, there are these 120lb robots that play frisbee in the gym" as an answer.

We might need a bit more of a "and check out how the industry professionals that mentor them use the same skills in X,Y,Z (A,B,C,D....)".