Your homeowners / renters insurance will cover your phone automatically, and will pay if it's lost, stolen or damaged physically. You will have a deductible on that, though, and many homeowner's policy deductibles will be higher than the cost of a phone (usually 1% or more of the home value). You can buy a personal effects policy for the phone that will cover the same risks but with a much lower deductible.
Paying the AT&T insurance makes no sense to me. $240 over the life of the contract to insure a phone that cost you $200 - $400 does not compute. Even if you have to pay more than the subsidized price for a replacement, it's still about a 50% rate on the cost of an unlocked phone, which is crazy.
Most retail insurance plans are giant rip offs. They make huge commissions on their sale, which is why they push them so hard. A good rule of thumb is never ever buy them.
Also check your credit card terms and conditions. You may well have insurance from them for a limited time.