Wouldn't people get more risk-averse and change the probabilities?
The amount of control you have over the probability of an accident long term is miniscule.
it doesn't matter how risk adverse you are, over 10k years SOMETHING will happen to you. Even a man in a vault is toast (literally) if an unknown volcano cooks him in place.
All you can do is not make the odds substantially worse, but you can never make them really good over a long enough period of time.