If the bat is not in a position that forces it to angularly displace (arc; the blur in the video) immediately upon launch, then you have slack or slop in your swing.
Wrapping the bat is one way to "connect" so that you reduce the slop. I suppose, like anything, you can over do it. But, Upton is not overdoing it.
Your assumption that it automatically makes a longer path to the ball displays a typical misunderstanding about the swing. Is it longer in distance? Maybe, maybe not. A guy who wraps will usually hit the ball very deep in the zone. Compare that to a guy who doesn't wrap and moves his hands forward before the bat arcs, (slop) I'd say the latter has the longer swing distance .It definately is not longer in time. It is much quicker than a swing without it.
The time it takes between decision to swing and bat blur is critical. A guy who wraps will usually have this time very short. A guy who doesn't wrap or maintain a 90 degree angle between the forearm and the bat will be slower. Some guys do this with the bat more vertical. Some guys do this with the bat more horizontal. And everything in between.
But, by the time you get to this bat/arm relationship and then load, the bat is often times what lay people call wrapped. Call it what you want. It is not bad.
A hitter with a clue, will have the feeling that he, his body, himself, is inside the arc of the bat. This gives a feeling of the arc being behind him. A good thing.
A hitter without a clue will have the feeling of being outside the arc. He will have moved the hands forward first (slop) and then the bat arcs giving the feeling of the arc being in front of him.
These images are very good at depicting the "inside the arc" feeling.