Automobile insurance is a big game of risk versus reward. While the concept of getting the "absolute minimum" auto insurance and then investing the difference between that and full coverage, makes financial sense, how long will you have to save/invest before you reach several hundred thousand dollars? You'll be getting the bar minimum in personal injury liability coverage, which will *maybe* pay for someone else to be in the hospital for a 1/2 day (perhaps a day at best).
The majority of the risk involved with automobiles is in injury liability to another person(s), and it gets pricey VERY quickly. Sure, you can argue the other person "can't get blood out of a turnip", but hospitals and insurance companies can have a lien filed against you in court for hundreds of thousands (if not millions) of dollars -- and no, bankruptcy doesn't get rid of it.
Also, paying for full property damage coverage (collision/comprehensive) on a vehicle that is over 10 years old actually starts to increase in most cases. The insurance company no longer wants that type of business so they'll gradually increase the costs. It's hard to explain in a short online post.
If anyone -- on a new or nearly-new vehicle -- is going to go the "cheap" route you need to plan on having large injury liability limits and an umbrella policy, very high deductibles on collision and comprehensive ($1000-$2000 range), then create a savings account to cover those deductible amounts.
Keep in mind, if you have a loan for the vehicle the lienholder (bank) will probably require a certain level of collision/comprehensive coverage with a low enough deductible so that they won't loose their @ss in the event the vehicle is totaled.