I tend to be careful too. That didn't stop me from breaking two iPhones accidentally. But more importantly it doesn't stop mechanical defects from appearing.
When I updated my iPhone 5s with iOS 9.2.1, Touch ID broke, and the phone developed an abnormal battery drain. Took it to the Apple Store and they said 9.2.1 exposed some previous undetected defect. I was not able to purchase Apple Care + because I bought it from a friend who did buy it, and it can only be purchased within 60 days of the original purchase. So Apple offered to repair it for $269.
Now, if I had purchased that phone with an AMEX or Discover card, I would have still been screwed because it was 3 months past the 2 year purchase date.
Also, I will not pay a fee to any credit card company to use their card. There are too many other options that blow AMEX out of the water. And you still have to pay the entire amount up front, or pay high interest rates -- and I'd rather put the money in the bank and earn interest on it while paying an interest-free, monthly payment. And I'm not sure if you've ever tried to get a credit card company to honor one of those warranties, but beware of the fine print.
When it comes to the iPhone, nothing beats AC +. If something goes wrong, everything is quickly and easily taken care of. Add to that the fact that Apple is selling 50-70+ Million iPhones a quarter. Quality control is good, but the odds go way up you will need extended coverage. Personally speaking, not counting accidental damage, I've had to replace every iPhone I've ever owned at least once under warranty, and a few twice. My current 5s was replaced after 11 months under Apple Care for a defective flash, and then a little over a year later the Touch ID/battery problem. Fortunately the SE came along in just the nick of time, so I don't have to pay to repair the 5s.