It does sound like the OP has had just about the worst luck, but appreciate people do experience this. Apple's customer service is amongst the best I have ever dealt with but I suppose if you are returning so many phones, they have to be weary. After all it could be a scam where the user is swapping tampered with iPhones on behalf of others or something like that. At least with normal experience you can rest assured that if you experience a hardware failure, Apple usually replace it with very little questions asked. The OP has an S4 now and after 30 days you have more difficulty returning a defective handset if you wish for a straight swap. I know HTC ask that you return a device 3 times before they consider replacing it and I've heard similar accounts for Samsung.
Sorry to hear of the bad experience, but I'm sure if you had persisted you would have got another replacement. The service is generally very good in my experience.
Sorry to hear of the bad experience, but I'm sure if you had persisted you would have got another replacement. The service is generally very good in my experience.