While I'm not really one that should give technical advice over the internet, I had a teacher once tell me that the more body parts that are moving (wrist, elbow etc.) to help the fingers is compensating for a lack of technique.
What? wrists, elbows, arms are all essential parts in technique from what I have learned. Try playing the second movement in Scriabins sonata no. 2 without a moving, flexible wrist!
I readily admit that my fingers alone can't do the opus 10 no. 2! So of course I look to see if other body parts could be of help! No guilt here. My only regret is that I don't have witch-like powers to move the keys with my mind.
Interesting. Maybe the reason wrist movement notation never caught on was that it was not precise enough. To be precise enough, it would have to say whether the movement should be clockwise or counterclockwise, and where on the circle of motion the fingers should be hitting the notes.
Is it really necessary to be moving at the wrist?
Just as we need to use the conformation of the fingers, we need no less to use the rest of the hand, the wrist, the forearm and the arm. - one cannot try to play everything from the wrist, as Kalkbrenner claims.
Chopin
In what way does that quote implies that the wrist should be flailing around,
Using the hand, wrist, forearm and arm don't necessarily entail 'flailing' about - yet another straw man of yours.
Just look at Garrick Ohlsson playing the Etude.