There is an inherent problem with advice on physical motion being given in words. You will picture a given thing when you say it, and the person reading it will picture something else and do that other thing. If you saw what they are doing, you would see what is going on and correct it. Many things can go wrong.
Just like the video is misleading because it doesn't have to be done all the time. My description that lifting the fingers can be done by the wrist is clear, it's intention is not to teach thoroughly (which should be obvious as my response was quite short) but to make one aware.
I said it is a small movement not some ridiculous angles. My comment is good enough to make students here realise that lifting the hand isn't just done with the elbow nor is that exaggerated motion require as these videos try to encourage. I don't care if people misinterpret, we are not here to give free lessons or write a thesis.
By chance, before I had my teacher, I read the "lift your wrist" idea and tried it how I understood it. That made a mess that took some time get behind and solve. For one thing, if you "lift your wrist", then if you do it properly, other parts of the arm will move, or in the very least, they are not held back because in your mind you are "only supposed to lift your wrist". These days if I do the motion, I also see small motions in the elbow and weight goes in and out of my fingers. That is a far cry from what I did originally based on that cue.
Really it isn't a complicated technique we make that motion when patting a dog or waving, wrapping fingers on a surface or so many other non piano movements. People should realise how the wrist moves in a nautral way. Try to play fast repeated chords pivoting at your elbow to withdraw the fingers and one will see how stupid and utterly ineficient that idea is.
Again I don't indent to support my writing with diagrams, videos, musical context to teach, that is absolutely unnecessary as I am not getting paid for such time invested. Offering opposing views to the video above is all that really matters to encourage experimentation otherwise.
The advice is probably not wrong, but how it gets interpreted and executed might be.
It is not "probably not" wrong it
certainly is not wrong. The videos can be utterly interpreted wrong too as there is no actual musical context.
None of us have seen the OP play which is the first thing a teacher would want..
To me it doesn't matter the videos posted is all that needs to be scrutinised and since the wrist can do the job the advice in that video is put to question.