You're presenting a false dichotomy. The alternative to our current system isn't solely "no copyright at all". It's pretty simple: reduce copyright terms to something much more reasonable. I believe the original copyright term in the US was 14 years. I'm sure we can guess why that has been raised several times since then: greedy corporate interests.
Sure, it's certainly debatable what the "correct" term length should be, but I think most people could be convinced to value the commons a bit more and agree that it should be significantly shorter than the current "life of creator + 70 years" (or for works-for-hire, 95 years from publishing or 120 years from creation, whichever comes earlier).
For copyright owned by individuals, why should a creator's children and grandchildren (and great-grandchildren?) be allowed to continue to profit off their ancestor's work, depriving the commons of history and culture? For corporate ownership, why should the company be able to profit for longer than the lifetime of anyone around when it was created or published? Hell, most companies aren't even around that long, so ultimately the copyright ends up being passed to several other companies that have no relation to the original owner.
But really... 14 years sounds reasonable to me. I would even say 25 or 30 years would be ok, if the consensus is that 14 years is too short.
We could also go with a limited renewal system, like is used for patents. Say you get 14 years, and if, after those 14 years, the work is still important to you, you can renew the copyright for another 14 years, or something like that. People and companies who still actively gain economic benefits from their work 14 years later will go to the effort to renew it, but otherwise -- what is probably the majority of cases -- it'll fall into the public domain.
Of course, copyright isn't just governed by US law: the Berne Convention, at least, attempts to govern and harmonize copyright to some extent, and it requires minimums of 50 years after the creators death for most types of copyrightable works. But this is all doable, with political will behind it. As usual, that's always the problem.