The main reason to use the wedge is so I don't have to play "catch-up" when the tree starts to lean back. By then it is really too late. Just a fraction of lean back translates to many pounds of wood in the top of the tree that has moved, and you have to move it back. Using a wedge is smart, and smart loggers use them. Most of the times, the wedge just lays there, and the tree falls without ever setting back on the wedge. But you are thanking your lucky stars when the tree sets back onto the wedge that you have in place, and not still in your back pocket.
I was told once that in Sweden, (Think that is the country) their liberal safety laws require a wedge bar (the one with the handle) be used in the back cut of every tree being felled, for maximum safety. Carrying a wedge bar around from tree to tree is not as convenient as a wedge in the pocket, but then the bar offers more leverage when tipping the tree that doesn't want to tip (in the preferred direction) on its own.