Don't throw the baby out with the bath water! Copyright as it exists today may have too long a term. But getting rid of it entirely would create massive problems. Film, music and books would become uneconomic to produce overnight. Things like GPL would be unworkable.
I don't think so. We already live in a world where anything playing on a movie screen has a digital equivalent easy to find for free; ditto music and books. Despite that, sales continue to increase every single year. While removing it from the underground would no doubt decrease sales, calling it "uneconomic to produce" is unnecessarily apocalyptic.
As for software licensing, the GPL and most licenses would become irrelevant, since the copying can now happen both ways.
It is true that I pay for things I could illegally obtain for free. It is not the fear of being caught that stops me, rather that I believe the creator should be rewarded so more good stuff is made.
It is not only individuals illegally downloading we have to consider. What production or publishing company will invest millions creating and distributing content if they can't make a profit? Very few I would think.
It is true that software licenses would become irrelevant as well. People who think software freedom is important (i.e. copyleft) would not be happy. On the other hand, software companies could also not sell proprietary software either. I guess everything would become a SaaS product.
