The FAA is not exactly moving forward on "self-certified" medicals. In the light sport aircraft category, a pilot can fly based on their own evaluation of their medical fitness. Years of operation under these rules have developed statistics that pilots, under modern medical treatment, fly quite safely under self assessment.
So it is reasonable to expand these rules to any category of flying that presently requires a third class medical certification from a doctor. Under the current antiquated system established in the 1940s, a pilot with manageable conditions is required to do frequent expensive additional testing for FAA doctors that, because they are miles away, substitute these tests for personal physical assessments of the pilots.
This testing basically constitutes a profit racket for the medical industry. And, as experience with Light Sport has shown, this does not contribute to safety in a statistical sense. Until fairly recently, the FAA and Congress were on course to establish more rational regulation.
Recently, the revisions have been abandoned. Apparently the medical profession has taken up additional testing regimen with the FAA, now focusing on sleep apnea, a condition that was not considered significant since the 1940s. However, since apnea might contribute to exhaustion or dozing off while flying, some are pressing for testing of third class compliant pilots.
Yes, that's right. Even if you pass the current medical exam, you may be sent for sleep apnea testing. This is an expensive test that can potentially bar a pilot from flying even if they have a mild case of apnea. Because this is the perfect case of a sleep disorder industry that makes a lot of cash selling CPAP devices (another racket) with physicians requiring onerous testing programs for pilots with mild or controllable conditions.
So, in the name of money, the FAA has abandoned self-certification for a testing lab bonus for doctors. And I would recommend investing in CPAP manufacturers. It's going to be a booming industry.