So you would rather have to have paid out-of-pocket the three times in the past 15 years for whatever happened?
I noticed that you didn't say what you had claims for. Hopefully it wasn't too bad, but what would you have done if you had a huge medical bill. Let's use your example of a deer running in front of your car, while you are driving on a highway at highway speeds.
First, your car would be totaled. No if's, and's or but's about it. The cost to replace all the airbags by itself would cause the car to be totaled.
Now, what if in spite of the airbags, you lost control of the car and impacted something pretty immovable, say, an overpass. We will assume you will survive, but have huge medical bills. Over 6 months, you could concievable incur medical bills of over $400,000, depending on the extent of injuries.
Now, do you have/want to pay all that money, or have the insurance company pay that money? If you are paying $1000/year for the insurance, it would take you 400 years to recoup what the insurance company will be paying out.
Plug in your own numbers. I do not like driving in states which don't require insurance. You may consider me stupid, but I'd rather share the risk with the other insured people/cars rather than risk the financial loss myself.