A cheap and effective foil to AI breakers. This card is trivial for a Corroder or other fracters to break, but against an Eater or Overmind this card is very taxing. At one influence this can easily splash in any deck that you can't fit a Swordsman into if you are afraid of AI or Parasite. Against a standard program setup, Wall of Static or Eli 1.0 are better barriers.
Also, if you are using Paper Wall for some reason, just use this instead. It costs 2 more but doesn't self-destruct.
(Order and Chaos era)
You'd use Paper Wall in the same situations you'd use Quandry: to force the Runner to dig for a breaker they don't need. If you're running Paper Wall, it should be your only Barrier. Likewise with Quandry and Code gates. But to your point, yes, Wraparound will achieve the same thing as Paper Wall while being much more expensive to punch through if their barrier-buster isn't a fractor.
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KitsuAeryn