Come on baby! Let's do the twist!
SD - I have had a rare first time student or two "carve" on day 1. It's extremely scary because they feel emboldened to advance their terrain choice to slopes where their carved turns place them in danger of collisions with other beginner skiers making 11s. I've found that it's just as hard to teach them to skid the skis as it to teach skidders to carve. With the right gear and the right terrain, I have taught first timers to ski without a wedge and without a taught pivot. Most will pivot either naturally or skid via a brushed approach (reduced edge angle for the speed to lose a carve). For first timers I don't get bent which approach they pick up as long as they have the ability to adjust their turn shape to avoid obstacles. We can work on rounding out their bag of tricks later. But to your points, most of my first time lessons are still wedge progression because there isn't a perfect fit of gear, terrain and student skills.
I'm a little amazed at the thread explosion here. DTP progressions work. Wedge progressions work. Either approach can fail if taught incorrectly. It really does not matter how the student thinks they are moving their mass to the inside of the new turn. And it does not matter a whole lot what an instructor literally tells a student to do to get that to happen. Sometimes you have to say green to get red to happen.