My biggest worry is I get distracted by something interesting and show up late to wherever I'm going. The rest, not so much.

You can't worry about an activity and stop doing it just because it's tainted with death. Everything you do is tainted with death... you just aren't that original, anything you're doing has already been done so many times that somebody's unlucky number has come up, just through pure probability. If you worry about it all, you get overwhelmed and wind up doing nothing.

Careful, responsible bike riding is pretty safe, and safe is boring. I'm not saying go out and take additional risks on purpose, but that your wife may be getting a distorted view of reality, here. Safe isn't newsworthy. Safe isn't something people make a fuss about. Every time a rider hits the road (or off road) on his bike, and arrives at his destination safely, nobody notices and nobody cares. It's only when he has an argument with a mac truck and ends up with his head in five pieces that people stand up and take notice. The news articles and the anti-bike types can ignore all those hundreds or thousands of rides where nothing happens, because they don't serve their agenda. A person legitimately trying to get a feel for how safe the activity is, they shouldn't be ignoring the boring.