No. Plain and simple. No. Doctors are not just spewing out diseases that match a list of symptoms that they have memorized. What you get with a doctor is experience based knowledge and skill.
Short of some sort of highly advanced automated full-body scan that a computer can read and identify abnormalities you will require that expertise.
The most you could do with a full set of internal sensors connected to an iPhone is get a list of conditions based on probability. That list will go from a cold to cancer.
And god help anyone with a combination of things that combined mimic something else.
As for AEDs: It does one simple task. It judges if you are in a life-threatening arrhythmia, and applies a shock if you are. That is 20-year-old technology. The box is as big as it is so that it is idiot-proof for an amateur using it. The actual technology can fit between the rib cage and the skin, and that's with other systems in place as well. An AED or an ICD/Pacemaker are great emergency technologies designed to react faster than an emergency responder. They are not remotely close to being an electrophysiologist. In fact, I was once misdiagnosed by my ICD and unnecessarily shocked. I was in an arrhythmia, but not an immediately life threatening one and it read it incorrectly. I was shocked, but all it did was make me scream and involuntarily jump back about three feet.
As for the quote in the OP, I know this isn't the context it is intended, but you already are the CEO of your own health, whether you want to be or not. You can demand every byte of data on your health from your doctor, you can get second, third, and fourth opinions, you can travel the globe until you get a satisfactory answer, and you can fire your doctor. If you aren't already acting like the CEO of your own health, then you are being ridiculous. It is your life and your body. You have to be comfortable enough to have faith in your doctor, and smart enough to walk out if you don't.