I feel that I understand something when I can explain it to
a rank amateur such that they will also understand it, but
one thing I have yet to understand is the purpose of the quenching
action in superregeneration, apart from thequenching itself.

How does the quenching of an oscillating stage yield a detector
that works for AM, FM and / or SSB, when the quenching frequency
is supersonic, and neither at the RF nor the AF frequencies?