Why do most instructors introduce speed control with a braking wedge?
I usually don't teach a braking wedge until the very end of the never-ever lesson. They do need it in the lift line, and they will figure it out anyway so I address it as we finish up. The first 95% of the lesson is learning how to feel secure while enjoying the glide, which a braking wedge will destroy but a "gliding wedge" will preserve.
I have them learn in a wedge because having them ski parallel on day one is especially difficult in the short time allotted for our beginner lessons. Their control over balance is too tenuous. Most of the beginner lessons I've taught are only 1.5 hours, and that impacts how I teach. I wish the lessons were longer.
I choose to teach them to manage their speed by doing two things - completing their turns and choosing the corridor width for their descent. They learn to stop by fully completing a turn (a "turn-stop").
We start by skiing in a circle. In a wedge they glide in a curve downhill, walk back uphill either side-stepping or with a herringbone ... repeat. They do this in both directions, over and over, until they can use the outside ski to make the turn in both directions. At the bottom of the circle I encourage them to be standing fully on the outside ski so they can move the inside ski to match. Some can let go of the support given by that inside ski and do it, others can't. But they know this is the goal. In the process of doing this circle they learn that at the bottom of a fully completed turn their skis bring them to a stop.
Then we line up and link these completed turns down the hill. They will not have done a straight run at all, so no braking wedge. All of this is on the terrain dedicated to first runs.
Next we go up the beginner lift. On this run they will encounter a longer, higher pitch. But they know that the tool to control their speed is a turn. We do a few completed turns one at a time finishing each with a "turn-stop." No braking wedges mess this up. Then we line up and link some turns, almost coming to a stop with each turn. Half way down we stop and discuss another way to slow the downhill travel - do a traverse between turns. Since the slope is big we can start skiing in a wider corridor, and work on changing those traverses with short turns into C-shaped wider radius turns. They are learning that they can use corridor width as well as completed turns to eliminate fear and enjoy the glide.
At the bottom of the run, approaching the lift, I introduce heading straight downhill in a wedge to slow down. This is the first time they do a straight run. At this point it is obvious to them that using a wedge to brake is not nearly as effective at slowing their speed as is a completed turn.
There are big reasons not to teach a braking wedge (which is different from teaching first turns using a wedge). Relying on the wedge to stop in that first lesson morphs easily into reliance on the wedge as a security blanket with weight staying heavy on both skis. I've seen it too often. Once that is embedded in their heads and in muscle memory, skiing parallel becomes difficult to learn.