To be very clear: I am not proposing instability training instead of training on stable surfaces, or as necessary or superior. And research here is sparse. The cited article is somebody spouting off their evidence free WAGs as fact and I have mine!
I think of instability training as supplemental for smaller muscles that are not the showy ones. Comparing squatting, Romanian deadlift, Good Mornings, or alternating single arm curl to overhead press, etc., on a balance disc to doing the same on stable ground is silly. While they are all compound movements they are accomplishing very different things and emphasize different sets of muscles, along with different sorts of neural adaptations. These are the non showy core muscles and adaptations that protect our backs and prevent falls.
My WAG based on basic principles of training specificity is that you get better at proprioceptive awareness by specific stress and recovery of that system, and likewise of the various long core and oblique muscles that stabilize movement on unstable surfaces.
First thing I find though doing my quick search for instability balance work and aging surprised me though! Improved executive function compared to stable surface work …
https://www.nature.com/articles/s41598-020-59105-0
Huh.
And yes balance exercise helps balance in older adults (for example).
In terms of the utility of “functional” whole body movements that he disses as fatiguing … kettlebell swings, Turkish get ups, and heavy carries (farmer carries) - that large volume of muscle fatigue is a big part of its point for hypertrophy! Same as why squats and deadlifts help arm gains. The hormonal response is generalized.
Of course I personally wouldn’t care much if there actually was solid evidence that sticking to his more limited lift selection gave better gains and there were no other advantages to doing these exercises too. I will still do what I have fun doing!