Had THE engine discard a push rod in solo X country days, my MAYDAY was handled through an overflight relaying to ATC, and the response and help was professional and reassuring. Obviously each scenario is different: 73 engine failure on take off, single engine over water, light twin in high terrain etc. Seems more an issue of when to call the MAYDAY rather than if... Our TO brief calls for " no further action below 1000', other than to raise gear, silence aural warnings and advise ATC" and that call for me will be a (calm) MAYDAY.. not only for ATC but for all other traffic in the vicinity to get a heads up. A case of as soon as practicable in other situations?
Operating largely in areas with limited ATS, and more to the point limited ability to set up SAR, or any other assistance, I'd get that Mayday out quick sharp and get the cogs turning, can always downgrade it. Again gives traffic in the area a heads up, and keeps the frequencies clear to relay your situation, progress etc.
Also operating in high traffic density areas, doesn't it alert everybody, not just ATC? Restrict all calls till a/c is assigned designating frequency etc.
Not sure why 'Mayday' = 'panic' ????
I also report ELT transmissions......
Glad to hear that a/c is ok.