There are people out there who understand the value of insurance and want adequate coverage at a inexpensive rates. In my opinion, these are the best clients. You don't need to sell the person on the value of insurance; they all ready understand it. In my opinion, it is difficult to work with people who don't fully understand the value of insurance. These are the people who usually want the bare bones minimum coverage at the absolute cheapest price. However, when they need to make a claim they are usually shocked to find out that they don't have enough coverage.
To answer your question, in the years I've been an agent here is what a lot of people overlook when they don't have adequate coverage:
1. Auto Liability Coverage: Some states have minimum property damage liability limits at $15,000. When someone carries limits this low, if they hit a new car and total it they will have a financial difficulty. I've heard of stories where a person carrying $15,000 liability limits hit a brand new Toyota Camry and totaled it. That brand new car was valued at over $25,000. This person was sued for $10,000 because they did not have enough insurance to cover the loss.
2. Replacement Cost on Home/Contents: In my own experience, many people overlook the value of carrying full replacement cost coverage on their homes. If a person carries ACV (actual cash value) coverage, they are only paid the depreciated value minus the deductible. I've seen claims where an insured had roof damage on a home insured for actual cash value. The claim payment was no where near the amount needed to replace the roof. This put a HUGE financial strain on the family.
3. Many people overlook other added coverage options in order to save money on their premiums. For example, rental car coverage is often overlooked. When they end up submitting a claim and having to take the car to the body shop, they are sometimes shocked to learn that they will be without a car for a week or more. And since they don't have rental reimbursement on their policy, they either have to pay a large rental car bill or have to go without one (assuming the accident was their fault).
The problem with auto/home insurance is that it is not a product people see, touch, feel, smell or use on a daily basis. It is not like buying a car or buying a house. If you buy a car, you can see and experience the difference between a $15,000 car and a $30,000 car. If you buy a house, you can see and experience the difference between a $150,000 house and a $300,000 house. A home and a car are tangible; you can see and feel them. You experience both on a daily basis. Because of this, it is easy for people to see value in paying more money for a nicer car or house. Insurance is different. You don't use insurance on a daily basis. You can't truly experience the difference between a auto policy that carries $15,000 property damage liability and a auto policy that carries $100,000 property damage liability. You can't experience a homeowners policy that carries replacement cost coverage and one that doesn't. The only tangible part of an insurance policy when they buy it is the premium. When you ask someone would you rather pay $1000 a year for great auto insurance or $650 for the state minimum, there are some people that would say $650 because it's cheaper. It isn't until there is a claim that people can truly experience the value of the insurance policy that they purchased.