Robotics competitions fit your criteria decently well. They are safe, have educational value, competitive and are decently high profile. More specifically, FIRST and Vex are both fairly wide spread.
I don't think that is high profile in the same way though. You will never be well known for doing well at FIRST since the highest level of competition only has ~6k entrants worldwide.
Even at the level of FIRST, I think there are some unhealthy things that come out of the competitiveness, with teams where professional engineers do almost all the work, or a small set of students get a lot more attention than others. But it has a tonne of great benefits despite some small issues.
Even at the level of FIRST, I think there are some unhealthy things that come out of the competitiveness, with teams where professional engineers do almost all the work, or a small set of students get a lot more attention than others. But it has a tonne of great benefits despite some small issues.