If you have duplicate insurance in any area of insurance, it can involve years of delays of payments and even the necessity to end up in court to settle who owes what. If you want to be covered by insurance for any category, you need to have one and only one insurer covering that category. A related example would be when you get in a car accident and you are insured, and the doctor refuses your health insurance because it was an auto accident...but the other person's auto insurance company doesn't settle...so you're bankrupt anyway because you're caught between two insurance companies waiting for the other guy to blink. When elephants contend, the grass gets trampled.
Even if the credit card didn't ask you to do this, it would just be good sense. A bank with all its employees and lawyers doesn't want to get in an unnecessary dog fight over duplicate insurance. That should tell you how much of a hassle and an issue it is. So that's why...