I also know that a number of pilots defer certain care as they know it will be problematic for their medical to proceed. So they 'postpone' seeking treatment, which as we know can be life threatening. This is a direct result of the regulations being unforgiving and cumbersome. I know if I report a mental illness I will be grounded indefinitely, then have to jump through CASA hoops to re-certify. Where in reality the decision should be the sole domain of the pilot and their medical professionals to decide, provide a written report to CASA that everything's fine and move on. Therefore the pilot knows they can seek treatment, be cured and get back to work when they know they are ready, which can all be planned.
I agree entirely with most of that.
My only point of disagreement relates to your statement that the perverse incentive is "a direct result of the regulations being unforgiving and cumbersome". It's actually a direct result of the way in which individuals in Avmed have chosen to interpret and administer those regulations. People with messianic delusions on a crusade in the belief that Avmed is the last bastion between aviation safety and aviation carnage interpret and administer the regulations differently than people who are able to comprehend what the objective evidence and objective risk data show.
And the mechanism which continues to have the single most profound practical consequences in the regulatory regime is always available to get around "unforgiving and cumbersome" regulations: Exemptions. That's why there are plenty of pilots flying 'legally' and 'safely' out there who are not obliged to tell Avmed anything and about whom Avmed knows nothing.