It is possible to pay for more insurance than the company will pay out. That too me is having too much insurance. If you have a home that costs 300k to replace but you insure it for $1,000,000, the insurance company is only going to pay the 300k to replace the home in the event of a total loss.
To me, this question is answered by a cost-benefit analysis in a specific situation. If I think I'm very healthy, I may choose not to carry certain health insurance policies, for example. Are we talking about homeowners' insurance? Are we talking about insuring a property for an amount higher than its value? Flood insurance on a property where it's not required?--Many people think it's a good idea to carry flood insurance for several reasons. What about liability coverage? What about life insurance on me if I'm 97 and not providing support for anyone? What about insurance for an extremely wealthy individual who can essentially self-insure?