Thanks Beer Baron. I think it is important to look at the history of a Mayday and how 7700 follows. Many aviation standards are directly stolen from the maritime environment. Nav lights are an obvious one. Rules of giving way etc. A Mayday from a vessel indicates that the vessel is in distress, not a passenger on board. As for 7700, on its own, if used after a Mayday or PanPan call it would be redundant. The net result being that an alarm is triggered on the desk of the FIR Manager. Imagine a situation where voice coms are lost then a received 7700 squawk would initially be interpreted as a Mayday, perhaps downgraded to Pan after further information is received somehow. From this extrapolation 7700 seems a strong response to an unwell passenger.
I have had a few unwell passengers on my flights and of course we do everything we can for them, diverting for quicker medical care etc but for the most part luck plays the biggest part. If you have a stroke or serious heart attack between Melbourne and Darwin your chances of a good outcome are low. I have two friends who work in emergency medicine, one as an AO and their tales are sobering.
Notwithstanding all of that, if the PIC wishes to squawk 7700 that is their prerogative. Once alerted ATC can easily ask them to return to their code.