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Steve Foley writes:

When you approach stop, a bicycle will fall over to one side or the other.
(unless yours still has training wheels).

As long as the rear wheel is powered and both wheels have traction,
the bicycle cannot fall over. The usual reasons for a bicycle falling
over are a loss of traction or a complete absence of propulsive power
to the rear wheel.

Exactly the same principle applies to motorcycles, scooters, etc.



And what, precisely, do you expect the "propulsive power" to be accomplishing
if the bicycle is stopped?

Do we reject, then, the notion that the gyroscopic stability provided by the
wheels in motion helps to keep the bicycle upright? It is only a question of
"propulsive power" available to the rear wheel (specifically) while both wheels
must have "traction". As long as this is present the bicycle "cannot" fall
over.

Have I resumed your argument correctly?