Most journals withhold the copyright, and the scientists happily relinquish it. They can distribute preprint copies of their article (very few do in life sciences) but not the article itself.
I would not say that most scientist happly relinquish it, but they trade off the prestige gained from publishing in the journal for the copyright.
The real problem is the use of journals as an arbiture of research quality. If it didn’t matter to your career if you published in Nature or PLOS One then everyone would publish in PLOS One. If you are more likely to get a job or grant by publishing in Nature then people will do almost anything to get their work into Nature. We are trying to solve the wrong problem by worrying about journals controlling copyright.
Sorry, i find it hard to imagine a scientist feeling sad that he will publish a Nature paper. You are spot on that we need a new arbiter. It's 2016 and we rely on this ancient system, it's no wonder that the elseviers of the world take advantage of it.
But the control of copyright is a real problem, and i think we underestimate how much it hampers science (esp. considering the wonderful things one could do with machine analysis of the texts)
I have not met a scientist (including myself) that was happy about giving up the copyright, but it is viewed as the cost of publishing in a “prestige” journal. Nearly all scientists would prefer to retain the copyright if they could and make their papers widely available to everyone interested provide it did not exclude publishing in a career advanacing journal.
