The bungy is designed to restrict the size of the wing. It's typically used to make use of an oversized wing rather than having to buy a wing that's properly sized for the application.
The amount of available lift is dependent on how tightly the bungy on it is put. The bungy is used to help streamline the wing so it doesn't "taco" around the tank(s) and flap all over the place. There are arguments that the "ripples" that the bungy causes on the wing surface causes turbulence, increases drag and reduces streamlining.
Additional concerns with a bungied wing is that some people claim that depending on how tight they are, it may be difficult to orally inflate if that becomes necessary.
Further, since the bungies would act to squeeze the air out of the wing in the event of a hole or failure, some argue that it is a safety hazard. In a typical non bungied wing, you could orient yourself so that the hole is at the bottom and trap air in the upper (orientation wise) part of the wing and thus retain some degree of lift.
In short, a lot of people prefer to use a correctly sized, non bungy wing and then carry some sort of redundant lift device such as a drysuit or a lift bag/smb to deal with any emergency problems that may develop.