Here's the first paper off the top of today's submissions to gr-qc: https://arxiv.org/abs/1803.11224
Is it right?
How do you know?
To whom should you send it in order to get an expert review?
Which of those people has an ax to grind with one of the authors?
Of the remaining people, who do you think you could convince to invest a day or more to carefully evaluate the paper?
Okay, so you got replies back from two of your carefully selected referees (after two months of badgering one of them):
Referee A thinks the paper is great, insightful, and advances the field, but wants extensive changes.
Referee B thinks the paper is derivative drek and should be rejected because his friend C has already done something similar.
Your journal publishes twenty similar articles a week but receives three hundred a week. The careers of the authors are partially on the line, as is the prestige of the journal, the attention of the readership, and the future submission of articles by prospective authors.
Good luck training a neural net to do this well. I suspect a neural net can be trained to reject the worst crackpots, but little more, without rejecting insightful but unique/important papers.
e.g.: https://www.nature.com/nphys/about/editors https://www.nature.com/nature/about/editors
The actual problem, which I think you implicitly identify when talking about Nature and Cell, is the "prestige" factor. As long as researchers are motivated by a prestige level of a journal b/c they may fear being ostracized by their peers or not getting recognition for their research - which has monetary and career costs involved - I think it will be very difficult to convince anyone to switch, regardless of how effective the platform could be.
I haven't thought about that problem before so I'm not sure how to address it as of now.