Could just as easily be the new outside ski though, which eliminates the angst associated with moving the whole body across the new inside ski and balancing on its outside edge till the fall line.
Well what the instructor did was show both ways and have us do each. So, do as you suggest above, which is pick up old outside ski, starting on old inside ski, rolling from inside edge to outside. Basically doing everything on the opposite leg of the white pass.
But, think about how that works exactly. How do you perform the opposite of a white pass? How do you get on the old inside ski? You need to have it pulled back to the right place so you can stand on it and and stand on that little toe edge. If you are just learning to carve, you probably don't have good control of the inside ski and will feel very uncomfortable trying to stand on it. Likely it is too far forward. So that is a pretty big ask itself.
The intermediate student has good control of the old outside ski and can stand on that at will. So what student will do is likely complete a turn and do a big traverse to get the old inside ski in the right place, then do the next turn. That traverse is a problem to get the sensation of linked carved turns. Big traverse in a white pass is not as big of a deal IMO. I could feel the 'a-ha' moment in the white pass vs. doing the opposite of the white pass.
I think the white pass is actually easier to achieve and pathway to linked carve turns. It forces you to concentrate on and control the new inside ski - which was definitely a big problem for me. Intermediate-ish students are used to thinking only about the outside ski.