In my state, uninsured and underinsured are optional, not mandatory. But you always want to protect yourself to the same extent that you protect others. Liability insurance protects others from your negligence and protects you from their claims. UM/UIM protects you from the negligence of others who didn't have the foresight to buy insurance at the levels you do.
The declarations page tells you how much each component of insurance costs for each vehicle. The highest is nearly always collision and comprehensive for damage to the vehicle.
The best way to save on car insurance: get rid of the BMW and buy a low-mileage used car that is at least ten years old.
I can agree only partially with your first 2 paragraphs. In your first paragraph, I can't say that someone needs always to protect himself to the same degree that he protects others. In the case of UM/UIM, I have a limit lower than my BI Liability limit but still higher than the state's minimum (Financial Responsibility, or FR) limit. I am more concerned about getting sued by someone else due to it being my fault in an accident than I am being able to recover damages from my own insurance company due to damages done to me by an uninsured or underinsured driver. Hence, the lower limit, something always permissible when buying UM/UIM.
I worked for 23 years in the actuarial field, specializing in personal auto insurance. I can tell you that BI Liability and Collision were almost always the two costliest coverages, followed by 3 other coverages pretty close together: PD Liability, No-Fault (if your state allows it), and Comprehensive. Comprehensive can be more costly if someone has a newer car, or lives in an area prone to losses covered by Comp such as theft or natural disasters. No-Fault can be more costly if the basic package is set at a high level. But Collision is always more costly than Comprehensive although their rates decline as the car ages, unlike what you find with BI, PD, and No-Fault. Their deductibles and the Liability and No-Fault limits also determine what you pay for each.
As for UM and UIM, there are 4 distinct coverages in this family. UMBI, Uninsured Motorists Bodily Injury, is the simplest. It protects you from injuries caused by an uninsured driver. This can also include pain and suffering. Many states require UMBI to be bought at some low FR. You can buy higher limits of UMBI, up to your BI limit.
UIMBI, Underinsured Motorists Bodily Injury, protects you from injuries caused by an underinsured (not uninsured) motorist. UIMBI is sometimes a mandatory coverage, like UMBI. But UIMBI has a wrinkle because how it applies can vary from state to state. There is a broad type of UIMBI, a more restricted type of UIMBI, and a third type between the two extremes. You are usually stuck with whatever type is set by your state.
UMPD, Uninsured Motorists Property Damage, protects your car from damages caused by an uninsured motorist, such as hit-and-run. UMPD is not always allowed in some states. In a few states, it is mandatory like UMBI. In other states, it is optional. Because its coverage overlaps with Collision, in some states UMPD is limited to non-Collision buyers.
UIMPD, Underinsured Motorists Property Damage, protects your car from damages caused by an underinsured motorist. This coverage is quite rare compared to the other 3 coverages in the UM/UIIM family. Because of this, I very rarely reviewed the coverage in the few states which allowed it to be sold.
