As mentioned above, it is not likely to be an accident that disables you, but an illness. I went from perfectly normal, working fulltime and hiking on weekends to bedridden in a matter of weeks. Then I was lucky enough not to die (though my diagnosis had a 5% survival rate with old treatments; I got an experimental one that worked) and was left unable to work at all for months. After about 6 months I was able to do a little, but no more than an hour at a time or two hours a day. It's been about a year of that so far, even though my treatment is over and I am now being monitored (still under active care.) And yes, I work from home as a programmer, do not smoke, barely drink, etc.
My company (which I own) provides insurance: short term for total disability between 30 days and 6 months (before 30 days we decided to self insure) and long term for 6 months to 5 years. However I discovered that they demand you apply for the government disability pension, which is taxable, and lower their (tax free) payments to you by the same amount, lowering your actual income. And once I started working again I discovered that they'll only cover you for two years if you're working part time, instead of the 5 years if you're not working at all. I intensely dislike my insurance agency. I recommend you do some research into these sorts of things.
On the actuarial side you can be sure that if you multiply out your chance of getting something you are paying a slightly higher premium than the odds would suggest. That's to pay for them running the program. But like life insurance and house-burning-down-insurance, it's all about "How would you cope if you needed it?" and I put it to you that you would not cope well at all. Especially when you're ill, it's not just you who doesn't work, typically your spouse doesn't either and you lean hard on family and friends. Had I died, my husband would have got my life insurance, but since I was lucky enough to survive, we really needed that income.