Why consider full coverage car insurance, as opposed to liability only?
It depends on both the value of the car and your financial situation.

For example, a $5,000 car may not seem a likely candidate for full coverage, but if your financial situation is such that coming up with $5,000 to replace it is a hardship, you should invest in full coverage, in case you’re at fault in an accident or the car gets stolen.  If spending $5,000 to replace the car wouldn’t bother you, then don’t.

Also, you have to look at it like a gambler and assess the value proposition.  For example, let’s say you have an older Honda Accord that is now only worth $6,000.  Your #1 consideration is that this car is rated the most likely car to be stolen.  Your #2 consideration is that full coverage only costs $200 a year more. The payoff, if your car is stolen or totaled, results in a 30-1 ratio of return on your investment. That is, you would receive $6000 for your $200 investment. 

In general, the odds you’ll have an insurance driving event in a particular year, whether a rock through the windshield or an accident, are 15-1. In short, if replacing a car would be a financial hardship on you or the payoff ratio is high, you should get full coverage.