I personally do not agree with this check.
The first thing that you need to do with a rough running engine is apply full carb heat.
Not arguing with your experience but this is 6 of one or half-a-dozen of the other.
If overly mixture was the culprit for the engine running rough selecting carb heat could cause it too stop.
But let's stop the discussion here, the point being that you need some sort of check/procedure memorized for these events.
FAST, AFeST, BUMP, BUMPFICH, GUMP, GUMPS, it's all trying to achieve the same thing.............memory items.