Quoting from that link: "One of the big challenges is discussing the costs and value added in managing peer review is that researchers who engage in this conversation tend to be amongst the best editors and referees. Professional publishers on the other hand tend to focus on the (relatively small number of) contributors, who are, not to put too fine a point on it, awful. Good academic editors tend to select good referees who do good work, and when they encounter a bad referee they discount it and move on. Professional staff spend the majority of their time dealing with editors who have gone AWOL, referees who are late in responding, or who turn out to be inappropriate either in what they have written or their conflicts of interest, or increasingly who don’t even exist! .... Much of the irritation you see from publishers when talking about why managing peer review is more than “sending a few emails” relates to this gap in perception. The irony is that the problems are largely invisible to the broader community because publishers keep them under wraps, hidden away so that they don’t bother the community."
I'm sure there must be some way to achieve this and also make the content freely available. But whatever system replaces the current one has to deal with these issues too.