Big Pistons, I marvel at your faith in the collection of stressed rotating and reciprocating parts, held apart by a microscopic film of oil without which it will destroy itself within seconds, that comprises an aircraft engine. And we are talking not modern highly-developed, superbly engineered, highly computer-controlled very well developed modern automobile engines, but an old technology air cooled 1930s engine similar to what used to power classic Brit motorbikes, only larger.
You say:
the Least Common scenario is for an EFATO in for an aircraft that has
1) no outstanding maintenance issues,
2) Has sufficient fuel, no contamination, and from a correctly selected tank
3) Shows no anomalies during a complete and comprehensive runup
4) Was checked for Carb ice before lining up for takeoff, and
5) The engine gauges where in the green and the engine was developing full static RPM at the start of the takeoff role.
The engine that part-failed on me ticked all those boxes. So did the Lycoming in the PA38 in which the guy I knew died when it stopped at 300 feet.