How could a mainstream commercial publisher make a POD, accept-anything imprint work without acting unethically and attracting criticism?
The publisher would be wise to enforce a strict "previous rejections required" policy when accepting books for POD publication, in order to ensure that the books which might have an excellent chance of commercial success were still published through the usual channels.
There are more details which would have to be considered, such as the possibility of recommending paid-for editorial services (and here the publishers' successful writers could opt in to provide a freelance service—I bet that many would welcome the extra money); cover designs (a standard template which was colour-coded according to genre could be used, unless the author provided their own); and the possibility of providing some sales and marketing support for selected books, and the scheme as a whole.
There'd be a conflict of interests if publishers referred the writers it rejected direct to their own POD imprints: but if several publishers set up such imprints they could together fund an umbrella organisation to govern them all (which wouldn’t take much—a carefully-researched website, plenty of information and resources, and someone to respond to queries), and refer rejected writers to that organisation for advice. This organisation could run much like the UK's Society of Authors: it would provide all interested writers with information about the problems inherent in publishing books with no editorial, marketing or sales support, in order to reinforce the message that this was not a route to billionaire-status; and it would add an extra layer of assurance that the writers knew what they were getting into.
What would this sort of scheme achieve?