Lots of people make poor decisions in crises.  Some panic, and don't make any decision at all.

Insurance for affordable things can provide emotional security:  If something goes wrong, the purchaser will not have to make a painful financial decision in a crisis.  Many people do not want to have the burden of arguing about money, or having to spend precious cash, or borrow money, or raid savings accounts, just at the time they are already reeling from another loss.  Having insurance "just take care of it" can save them an emotional double-whammy.  

Several kinds of insurance fill this perceived need:

 * Dental insurance.  If you have a serious tooth-ache, do you want the fear of the full cost of a root canal to discourage you from getting it taken care of?
 * Comprehensive automobile insurance.  Even if your car is old and cheap, do you want to have to worry about the cost to fix or replace it when you have just survived an accident? or discovered it stolen?
 * AAA.  It's nice having a superhero on speed-dial.
 * Jewelry insurance.  If your wife breaks her diamond, do you really want an argument about how to find the money to replace it?
 * Phone theft/breakage insurance.  If your phone gets smashed, wouldn't you like to just make a call, and have it taken care of?  Shopping for a new phone while your old phone is out of commission might not be a pleasant experience.
 * Pre-paid funeral services.  If you make all of your final arrangements ahead of time, your funeral can be the way you want it to be.  Your grieving relatives don't need to worry about how expensive the funeral home is -- you have taken care of those choices.  (Plus, pre-paid funeral services don't suffer the delays of probate and ordinary life insurance policies.)