Beyond the flawed logic of the Catalyst, why was this never explained?

Leviathan survived just like some termites do... moving over to a different place.  The point is that some survived.  The Reapers were not successful in eliminating every single ant in two separate cycles.  That's a fact presented in the game.

It's also a philosophical fact that it's just not easy to destroy every single ant regardless of the method used.  I'm not suggest that the wave would "selectively destroy only a handful of Reapers" but that doesn't preclude the wave just "missing some."  Even a raging forest fire misses some trees... it's not selective when it does so; but neither is it so completely thorough that it kills absolutely everything either.  In literature, most post-apolyptic stories rely on that idea... that someone survives regardless of the size of the nuke dropped on the planet.  Why, all of a sudden, should I believe that a single crucible would be so effective as to eliminate every single Reaper across an entire galaxy with 100% certainly that absolutely none would survive... just because that's what the success of the destroy ending depends on?  My response... How convenient!   

Shepard's doubt expressed in the pre-EC ending is completely ambiguous and therefore open to whatever the player imagines it to be.

I honestly don't care what ending you select and how you might rationalize it.  This one leaves an opening for me to rationalize selecting that ending in a different way.  Nothing says I have to select the same endings everyone else does for the same reasons everyone else does... or else it wouldn't matter if Bioware didn't write any player agency into their stories at all because all the peer pressure that goes on around here would just override it all anyways.

If you read the rest of the post, you would know that is not the case. But I admire your stubbornness to look for a fight that isn't there.

And yet the game explicitly shows the wave of all 3 kinds literally covering the entire galaxy.  The Reapers are pulling the equivalent of trying to step on every termite. The ending waves are more like dropping napalm on the entire city and burning it to the ground. At least in terms of coverage.

If the game wanted to suggest any Reapers survived, I'm sure it would have shown it to be the case. Instead, it showed Reapers falling over inert. It isn't equivalent to causing extensive damage. It creates a reaction (we see the swirling red energy around the Reapers) that causes them to cease functioning. If it were pure damage, then the world around them would likewise be damaged.

The only way a Reaper could survive is if it were away from a relay. Hardly impossible but I think it's a leap. We're supposed to conclude that the Reapers will no longer be a threat. A surviving Reaper would be a threat.

I doubt Hackett would refer to them as being destroyed, for a start, he's a military man who has been fighting a threat that emerged from dark space. I really would not be surprised if he had some expectation of there being more Reapers out there waiting. By saying they were defeated it simply refers to those that they were fighting. Not that I believe any are hiding, but I believe that Hackett would suspect it.