I think you'd need a very radical overhaul of how science works to replace the scorekeeping aspect. I don't think a Github CV is a good analogy to how this could work, because academic science is interested in hiring leaders (i.e. people who can get funded), not contributors. I think realistically you would need to change how science rewards/emphasizes certain activities first, and then publishing would follow. That would be a good outcome for science, but I think it'll be awfully hard to get out of this equilibrium.
edit: I'm curious what you think of the PubPeer model. That's obviously different from what you're envisioning, but thematically I think there are some similarities.