You talk as if most BasicMed-compliant pilots are going to an AME for their BasicMed exam. I’d question whether or not this is true. I thought the intent was that the BasicMed exam would typically be performed by the pilot’s primary care physician, the doctor who (at least in theory) best knows the pilot and their medical issues. That’s certainly the way I do it.
Of course, it’s possible that a pilot could go shopping around to different doctors until they find one who will pass them, and perhaps this happens, but if it does, it doesn’t seem to be having an impact on safety.
I also wanted to comment on your confusion about why BasicMed recipients might have generally higher death rates than third class medical recipients. That didn’t surprise me, as I am sure that many BasicMed applicants are pilots who do have a health issue of some kind – perhaps one where they’re worried about approval of a third class medical, or perhaps one where they’ve just tired of the time, significant expense, and stress of having to reapply for special issuance every two years.
Pilots with no underlying issues of concern to the FAA might find it just as cheap and easy to keep going the third class medical route. But pilots on special issuance are probably crazy to stay on that hamster wheel if their flying needs will be met by BasicMed.