Not everything needs insurance. And real insurance has costs that are pretty close to the expected average risk, while buying things just in case could be much more.
And the 1/10000 calculation was not the chance of huge trouble, it's 1/10000 to be unable to get a ride to have any trouble at all. The vast majority of those incidents are going to be worth much less than a thousand dollars. The chance of an event being that major is another factor of 1% or less.
Am I going to pay a thousand dollars a year to avoid a one in a million chance each of missing some important business meetings? Definitely not. Especially when other factors I can't change are much more likely to make me miss a meeting.
I mean, if I had odds that low of major illness I probably wouldn't pay hundreds of dollars a month for health insurance either!