Your proposed solution will not work because the sibling journal doesn't have the same paid support staff to do the unpleasant work that academics do not want to do. The unpleasant work includes administrative, first pass screening, copy-editing, typesetting, etc. I wrote a previous comment about this: https://news.ycombinator.com/item?id=16738497
Therefore, the zero cost sibling journal wouldn't even get started by (most) academic editors because it imposes more labor they don't want to do. Yes, publishers like Elsevier and Springer are vilified ... but they also have paid staff and infrastructure to support the papers editors.
Because internet discussions have the constant repetition of "the reviewers are unpaid" (which is true), it creates a distorted mental model that the prestigious journals have "no paid staff" (which is not true). The publishers' paid support employees helps the unpaid reviewers.
An interesting journal that might seem like a counterexample to the support staff labor puzzle above is JMLR. But in an essay that explains how JMLR is able to function (e.g. offload typesetting and out-of-pocket expense of copy-editing to the submitter instead of the publisher) ... that same essay also explains why other journals haven't copied JMLR's model. (Analogous to your "sibling journal" proposal.)
Excerpt from https://blogs.harvard.edu/pamphlet/2012/03/06/an-efficient-j... :
>Does JMLR’s success and efficiency mean that all journals could run this way? Of course not. First, computer science journals are in a particularly good situation for being operated at low cost. Computer scientists possess all of the technological expertise required to efficiently manage and operate an online journal. Journal publishing is an information industry and computer scientists are specialists in information processing. Second, the level of volunteerism that JMLR relies on is atypical for the entire spectrum of journals.
Thus, the academics and editors at non-compsci journals such as Nature and The Lancet do not have comparable culture of information systems platform management, computer software skills of typesetting, volunteerism, etc that JMLR has. And the key is that they have no incentive to do so since the publishers already give them infrastructure support without imposing extra labor on the editors.