And telling them they're using a tonal system that lets them modulate 12 times in the same direction and end up where they started is useful?
I don't know anyone who does that, Jack.

That's the only capability a circle gives you that a ladder doesn't.

If you have a final cadence in G minor with an F sharp in in the melody, the usual explanation of what it's doing there is that it can be seen as part of a Dmaj or D7 chord. The circle of fifths says you could also see that note as a G flat. Does that create any additional understanding? Is it actually likely that any chord with a G flat in it would fit at that point?