There’s not a different radius to different wrist motions — the pick is just as far away from the fulcrum going up and down as it is going side to side. If I’m understanding you correctly.
I think the difference is neuro-muscular of some sort. The muscles involved in doing flexion-extension are just stupid fast. Ran across this example today. But if you’ve ever done fretboard tapping with a pick using your wrist, you’ve probably already experienced how crazy fast it is:
I’m not explaining myself correctly 
so I’ll try again – and my thoughts may be off. To demonstrate the “radius” idea, holding a pick, hold your hand inline with your wrist, and rotate your forearm. The pick doesn’t travel much. Then, bend your wrist 90 degrees, and do the same rotation. The pick travels a lot, describing a much wider arc. This doesn’t matter if the motion is translational, but I’m sure you have some rotation in there too. Maybe. Who knows?
A “fulcrum” is used when describing a lever – I’m not sure what you’re referring to. Do you mean the “origin point” of the motion, i.e., that point that doesn’t move? Terminology is tough.
I had actually thought that this had more to do with the pick being much more rigid than finger flesh, so the fretting can be accomplished far more quickly – but I agree the wrist does it better.
Cheers! z
Aha. I get it, but that’s not wrist joint motion, that’s forearm joint motion. What we’re taking about here is wrist motion. The arm does not rotate, but stays fixed. Only the hand moves.
However to use your example, even in the case of forearm motion, the speed of the joint itself is unchanged regardless of how you bend the wrist while you do it. The joint motion itself is the two bones rotating around each other, and does not become any faster when the wrist is flexed. There is a maximum frequency you can change direction rapidly, and that’s it.
Right, I was thinking that the rotation wasn’t already maxed out, for some reason, but that’s almost definitely not the case.
Have you made any further progress with this?
I love this band so much 
Still listening to them/watching their video clips every weekend.