15 grand is enough to live off of... for a year... if you're frugal, have no debts, and your amazing thing doesn't require any startup expenses. It's not enough to make risk aversion meaningfully less important. I suspect most 21 year olds would still do the same things as they do otherwise, just with a marginally better lifestyle.
On the other hand, I actually like this idea. It would help people escape abusive situations, and I generally think it's fairly ridiculous how we ask young people to live on so little money while educating themselves. I just don't think it would cause many people to "go do something amazing".
I would prefer just taking every 21 year old and saying "here is 15 grand, go do something amazing".
I don't know what the results will be, but a fair number will be worth the risk.