There may be a contrived way out of this conundrum, but I think really the most sensible way is simply regulation.
We've had a ton of scientists sacrificing their own individual reputation and relationship with publishers (and of their groups) in name of something everyone agrees but few really stand up for, because the personal gains are almost exclusively negative. That's textbook use case of regulation.
I don't know specifically what should be done but perhaps a requiring publishers certain obligations (e.g. responsibility of maintaining papers for a long date and turning them public afterwards); or maybe simply a universal obligation to open publications after say 5 years.
People fear this will compromise quality or sustainability of publishers. But the community need publishers. It's a tag of credibility. So if publishers are into trouble (and they're really needed) they'll find a way by e.g. demanding payments from publications from the most wealthy labs.
The NIH, Howard Hughes Medical Institute, and a number of other major funders of science both in the U.S. and U.K. already require papers funded with their money to be open access after 12 months.
The problem is that whether or not a paper is Open Access, "Data is available on request from the author" may be an undocumented bit of spaghetti code, may be stored on a Zip disk around here somewhere I'm sure, or may just be lost.
Regulating "You must make your data accessible, and maintain it well" is much harder to implement, and much harder to check. Some grants now have sections describing what will happen to the data etc., but right now there really is very little reason beyond their own personal desire for researchers to maintain good quality software and data repositories.
We've had a ton of scientists sacrificing their own individual reputation and relationship with publishers (and of their groups) in name of something everyone agrees but few really stand up for, because the personal gains are almost exclusively negative. That's textbook use case of regulation.
I don't know specifically what should be done but perhaps a requiring publishers certain obligations (e.g. responsibility of maintaining papers for a long date and turning them public afterwards); or maybe simply a universal obligation to open publications after say 5 years.
People fear this will compromise quality or sustainability of publishers. But the community need publishers. It's a tag of credibility. So if publishers are into trouble (and they're really needed) they'll find a way by e.g. demanding payments from publications from the most wealthy labs.