An important issue I see with crew requesting medical assistance on flights is that they immediately accept the bona fides of whoever puts their hand up. I have never seen any procedure followed to establish if the person, in fact, has any medical training whatsoever. And staff singling out passengers with "Dr" on their boarding passes is not reliable at all since even a floor cleaner could sign up as "Dr" xx_XX on their QFF membership without any qualifications at all, medical or otherwise. A fraud with a celebrity-seeking personality could potentially start sticking needles into someone just because they volunteered.
This then opens up the question of liability if something went terribly wrong because crew let an unqualified person treat a fellow passenger.
This raises a concerning aspect. If I am conscious perhaps I could ask to see their practice licence. Of course, even with that, they may be a psychiatrist which is useful if I'm freaking out, but they may be a bit rusty on some other problems.
Surely there is an extremely remote chance this could happen. The chances of some falling sick on board are reasonably low to begin with, overlay this with the chance that someone is on board who might choose to misrepresent themselves as a medical doctor, it becomes an extremely small risk. [to put into context, I'm personally much much more concerned that the taxi driver who is driving my taxi at the end of the journey is actually is legitimately qualified and capable of driving that taxi safely, than falling sick on a plane and being attended to by a fake medico, and therefore would not expect airlines to put in a foolproof system of verifying qualifications. Sometimes you just have to rely on people in good faith].