Healthy life expectancy is only 75.0 max (in Japan)
If we expected to live much longer than that, we might be more cautious of accidents.
If you only have ~10-50 years to live, you might be prepared to take some small risks to save time: cross the road 100m in front of a speeding vehicle... it's a tiny risk and you might die of an acute disease tomorrow anyway.
If you have ~1000-unlimited years to live, people might generally take fewer accident-causing risks: the cost of an accident is hugely greater.
Then again, who knows? Maybe a society of immortals would need to take more risks in exchange for status.
But, you essentially decide your own level of accident-risk and I'm sure you could get it way down from 1/1656.