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1) First, most researchers at universities or other institutions have always had unfettered access thanks to a site license. It would be pretty hard to find a real example of a university researcher who couldn't see something.

2) There may be a few researchers who don't have unfettered access. Perhaps they paid $40 for a copy of a paper. Given the high cost of other parts of research labs, I find it hard to believe that any real possibility of curing cancer was halted because someone had to pay $40.

3) It's possible to imagine the opposite being the case. Perhaps someone had a key insight in a clever paper and decided to distribute it for free out of some info-anarchistic impulses. There it would sit in some FTP directory uncrated, unindexed and uncared for. Perhaps the right eyes would find it. Perhaps they wouldn't. Perhaps the cancer researcher would be able to handle all of the LaTeX and FTP chores without slowing down research. Perhaps they would be distracted by sys admin headaches and never make a crucial follow up discovery.

The copyrighted journal system provides curation and organization. Is it wonderful? Nah. Is it better than some ad hoc collection of FTP directories? Yes!

Your opinion may be that this scenario would never happen. In my opinion, this is more likely than your vision.