wouldn't
Run -> WD forward -> Turn (or start dashing back) -> WD back
be faster? It does the same thing without having to get to the edge to turn around
This is actually a little slower than lean dropping, at least for characters whose dash is faster than their wavedash. Here are a few edgehogs that are faster though:
All: dash -> wavedash forward -> pc drop (hard)
Characters whose wavedash speed exceeds their dash speed: wavedash backward all the way to the ledge
Fox and Falco: dash -> shine -> turn around -> wavedash back
Fox: dash off the stage -> side-b at the ledge (only faster if he grabs the ledge before the actual attack starts)
Mario, Doctor Mario, Fox, Falco, Link, Young Link -> dash -> short hop -> turn around pill/fireball/laser/arrow -> ledge cancel and slide to the edge
Mewtwo: dash off the ledge -> up-b to sweetspot
Yoshi: dash off the ledge -> turn around and double jump
Yoshi: dash to the ledge -> up-b at the ledge
Link, Young Link, Bowser -> dash to the ledge -> up-b at the ledge
Jigglypuff: dash off the ledge -> sing or reverse rollout
Pikachu: up-b to sweetspot the ledge from the stage (this is probably about the same speed, actually, and for Pichu, this is slower)
Marth: dash -> short hop and bair
Samus: super wavedash toward the ledge while facing it
There are probably a few that I'm missing. Of course, each of these have advantages/disadvantages other than speed. Also, the lean drop can be done a little faster than shown in the video. To do them more quickly:
1) Minimize the distance between the point where you stop dashing and the ledge (lessens the time spent "sliding", which is slower than dashing).
2) Minimize the time from where you start the leaning animation to where you start dashing backward.
3) Minimize the time between starting the dash backward and starting the wavedash toward the ledge.
4) Fast fall once you leave the ledge.
Of course, doing each of these makes the lean drop more difficult to perform and therefore more risky. So I guess it would be wrong to say that the lean drop has one set speed when the speed of the lean drop depends on the technical skill of the player.