Dislaimer: I am a terrible reader due to and eye/brain connection issue, so I didn't read all the replies. So forgive me if I am repeating something someone else mentioned previously. Hopefully I can add something new.
I was thinking about why the change from extension to flex to release....
If you extend to release, that means the legs were flexed before the extension. With older skis, the edge angles were a lot smaller, so the g forces also a lot smaller. So skiers could withstand the lower g forces with flexed legs...With modern skis, edge angles are a lot bigger, a lot more g forces, and you needed a pretty straight outside leg to withstand these forces.
So if at the end of the turn the outside leg is straight, it makes sense to flex it to release.
"With older skis, the edge angles were a lot smaller, so the g forces also a lot smaller."
Back in the day the release of the turn was taught, in the terms of Georges Joubert as "avalement" (absorption) and "replement" (I honestly don't remember the direct translation in context but the dictionary calls it 'replanting'). We would learn it as up-unweighting and down-unweighting. Down unweighting was largely situationational. Most recreational skiers, due to the equipment available until the 90's used up-unweighting to initiate turns so the skis could more quickly be pointed down the fall line, where it was easier to engage the edges. As the turn was finished the angle of the slope contributed to increasing edge angle toward the end of each turn. However, "carving" back then would (for the most part) be called "scarving" today. Most of us didn't make railroad-track turns on older straighter skis. The upper portion of the turn was rarely carved. Of course, up-unweighted initiations are extensions. One of the first, most recognized ski teachers teaching railroad-track turns was Warren Witherell, but was largely ignored by the rank and file skiers and instructors.
With today's skis, our approach to the turn needs to be different because of the way skis are built. We often make railroad-track turns (or at least try) and try to begin true carving of the turn very early after initiation. There are a lot of reasons for retraction at initiation, several of which I will omit for the moment to keep it as simple as possible for this response. But if you think about it, if we want to carve the upper portion of the turn, that first phase of the turn is where
the forces create the least amount of naturally occurring pressure in the turn. Keeping extension in reserve at initiation allows the skier to extend into that upper portion of the turn. Retracting the new inside ski as the turn develops allows continued pressure transfer to the outside ski. The natural forces at the end of the turn provide plenty of pressure where you do not need to keep a fully extended leg throughout.
Retraction, as one ends one turn and initiates another, provides for smooth transitions from one turn to the next. In other words, one extends where you want to maintain good ski-snow contact where natural pressure is largely absent and flexes/retracts where there is sufficient, or too much pressure- where one doesn't need to extend. A lot depends on the dynamics of the situation. Note that this is a general statement because foot-to-foot flexion/extension adds another dimension to the conversation.
While I couldn't find an adequate description of "replement", I thought some might find Avalement interesting.
Avalement and Georges Joubert
Again, I've left a lot out as my reply already has become a bit lengthy.