I did think about it, and I see the fatal flaw in your reasoning.
The moon orbits around the Earth. That means your line from the Earth to the moon also represents half the motion of the moon if viewed edge-on to its orbital path. As you can see, there will be times when the moon is "alongside" the Earth rather than above (or below) the plane. If these times coincide with the moon being between the sun and Earth, there will be a total eclipse.
By the way, it took all of about a minute of searching and thinking to debunk your so-called "conundrum".