Insure or not to insure. You take the same bets as you do in Vegas. You could lose, win, or lose big. In the long run you will lose.(someday)
The statement: "Most accidents happen at or near your home" does not mean driving in stranger places are less likely to cause an accident. The only thing the statement qualifies is a law of probabilities. You drive in and out of your "home" at least twice a day. You add all that up and you will more likely get into an accident near your home.
Again this does not mean that when you are somewhere else driving on roads you have never driven is just as safe or less dangerous.
Personally when I rent a car, I use an AMEX with Primary insurance and I also buy the Rental SLI to protect against 3rd party claims. I would rather not have my personal insurance deal with that or risk my rates going up. I don't rent that often so it makes financial sense to me.
If you do rent often then perhaps you should let your personal insurance take the responsibility for all your rentals.