As for how that might affect psychology: honestly, I'd love to see how the world might change if people adopted drastically different attitudes towards death, but I don't think it likely that this would produce far more risk aversion than we have today. Not least of which because I see no signs of tobacco companies going out of business.
For myself personally, I'm not going to stop leaving the house, but I certainly have no intention of taking up hobbies like hang gliding or motorcycle racing, any more than I plan to start smoking. (Side note: for an interesting measure of risk, see https://en.wikipedia.org/wiki/Micromort) I don't think that level of risk aversion qualifies as "a pretty frightened bunch not leaving home much".