I can make roundabout 5 to 6 "liftings of the wrist" per second. But then I'm not relaxed at all. And for many, many pieces, that's waaaayyyy too slow.
To play any percussive instrument you need weight trasmittion.
The shape of the bone of the arm and the fingers is such that they work as arches trasmitting the weight from the keystone to the pillars.
Percussive weight trasmittion needs also a pressure force which comes from exerting weight from above to below.
That's it percussive playing is based on a falling weight which creates a pressure force.
The falling weight is that of the hand and forearm.
If the structure of playing is static no falling weight can be trasmitted through the joints.
Also as long as the structure is static the muscular activity is static too which means that tension is being accumulated by not allowing any dynamic muscular activity of shortening and lengthening (hence the breathing)
If you look at a drummer you'll notice the drums sticks goes up and down.
If someone tries to play with just the fingers (i.e. lifting the fingers high) he/she will soon visit an hand doctor but nonetheless the movement is up and down.
It's impossible to play a percussive instrument without an
up and down motion.
The point becomes therefore what the pivotal of such up and down motion should be.
Focusing the up and down motion on the fingers will lead to discomfort, pain and injuries. The reasons are many but the main ones are that the movement is too strenous for the small muscles and tendons moving the fingers and for the joints and that if we rely on the fingers we never allow a completely reset (shortening) of the arm muscles contracting through the piece.
The up and down motion of the wrist (which shouldn't be thought as something isolated in the wrist but as a motion of the whole arm, wrist and hand) is that moment in which all contraction is resetted to allow the release of tension before a new striking (from above) impulse.
It's so clear in singing that we can't sing the whole piece on the same breath impulse but need to catch our breath periodically i.e. starting many new impulses periodically and it shouldn't be less clear as far as piano playing is concerned.
We can't play a piece on the same impulse
We can maximum play 5 notes on the same impulse before a resetting needs to occur and a new impulse needs begins.
The lack of phrasing would be one note for each impulse (meaning that between lifting of the wrist there's only one note) but only staccato would need that.
Basic phrasing would mostly involve 4 notes for each impulse or 3 notes for each impulse depending on the rhythm.
With singing an Allegro would allow 3-4 bars for each breath impulse while it would be 2-3 bars at slower tempo.
Of couse just like when singing the impulse is not "huge" and you don't just catch a huge amount of breath making an inhaling sound but actually breath a little and make the impulse fast and small the up and down keystroke in playing is not "huge" but small and fast.
Topic: Bach Three Part Inventions, No. 12 & 15