Opening and closing the ankle has nothing to do with lifting the toes/foot which is the movement under discussion.
The toe lifters are getting further and further from actually lifting the Toes/feet and making the discussion irrelevant. Now it's a cue, wiithout lifting? Next it'll be " I think about lifting my toes and close the ankle." Fair enough, but you're not lifting.
Claiming anyone who opens and closes their ankles is doing toe lifting is ludicrous.
I'm not sure if you coach/teach, if you do often you would notice that most push down on their toes, lean back, lever on the back of the boot (for many reasons). What's ludicrous about that?
If you're stuck in the back seat lifting the feet ain't gonna move you out. It's just going to put more weight on your heel and lock up your ankle. It may work as a cue for advanced skiers, that's different.
But backseaters toes are probably clenched. So lifting and wiggling the toes is a good idea to free up the foot/ankle.