In my experience:
This can be done to spin an attacker around and grip them by the throat with the other hand controlling base of the spine, either gently or to crush the windpipe, but can also be used to initiate a chokehold. Many practitioners are sloppy about sinking the elbows, and thus trivially unbalanced in fixed-foot pushing.
This is the setup to the main push of tai chi, and is usually done with dual, outward to downward circular counters. If you can trap the elbows, you have complete advantage for the followup push.
(Important to use rooting, where the forearms are "heavy" such that the opponent can't kick the knees in free stepping pushing.)
- Controlling the hip or knee
Controlling hip disrupts the root, and can be used to spin the opponent (though less optimal than using the elbow b/c the hands are not as well positioned for followup.)
Controlling the knee disrupts the root, focus can be applied to bend it the wrong way (ungentle-using instep in a cross step/kick to the opposite knee), or the back of the knee can be stepped into to force it to the ground. In Grasping Bird's Tail, the knee can also be used to push the opponents knee while applying the drag.
Controlling the joints in general is the primary objective
No matter how big or strong the opponent, they can't do anything if you take away their leverage by controlling the joints, and controlling the joints doesn't require much force, b/c you're never going force-against-force in wudang, rather continually adapting to counter any force from any direction.
Finding the center and pushing into it
Every push, well executed, is done in this manner, whatever the application. This is also how one uproots, and is the reason tai chi must be practiced in a relaxed, calm manner, so the practitioner can "feel" the opponent's center.
The core techniques are using the waist, sinking the joints and emptying—everything else is corollary.
Essentially, this or that application must arise naturally, without thought, which is why so much emphasis is placed on repetition of forms and applications, even though Tai Chi is a method of movement, not a set of forms and applications.
It's ideal to make contact with middle of the forearms, as opposed to the wrist, because wrist-to-wrist opens up wristlocks. By contrast, where you stick to an opponent's arm with your forearm, your hand is free to flick (eyes), push (torso or hip) and control the elbow.
In bagua push hands, which is a form of arm coiling, striking is expected. Here, use of the forearms is equally advantageous—you're already inside your opponent's guard when you gain advantage for a strike.