Your story is not that unusual. BMX is BMX... it's all about risk-taking, and if you haven't got brakes on your bike, you've got bigger balls than the next guy.
Having said that, the bravado can have fatal consequences, but not in a way that you would first think. Last week, one of the world's top BMX riders died in hospital after he was injured trying to jump into a hotel swimming pool from his fourth or fifth-floor room. He miscalculated the landing and suffered fatal head injuries. Ironically, he had just finished shooting video of some absolutely monster jumps than probably peaked at the same height as his hotel balcony.
Anyway, easy to say, I know, but your kid probably will be fine. Jump on him about the brakes, and he will find something else equallly as dramatic to do or not do, or remove from the bike. You won't even have a clue about the height of the jumps he has tried or will try, or the tricks he's turning on the local half-pipe.
And yes, seat hard down is de rigeur and has been for years, along with the tiny chainring.
Get with it, man!!