And it's not their own reputation that they sell; it's that of their (often paying) authors, and of their (usually voluntary) reviewers and editors.
It's a very comfortable position as rent-seekers for the publishers. And it keeps working because the authors get a needed (for tenure, grants, etc.) boost of their own reputation as well, and because reviewers get pressured into doing the work via arguments like
> every scientist who wants to publish in these commercial journals are also obliged to review 2-3 papers for every paper they intend to publish, otherwise the system would not work.
Good on the author for not being coerced by that, nor misleading themselves they can "engender small and positive changes from within". They're not abstaining from reviewing altogether, so if "the system" would not work, there would still be ways for works to get reviewed and authors to get their stamp of approval. But maybe, just maybe, this time without the middle man.
(Disclosure: I work on https://plaudit.pub, one of several attempts to establish alternative means for researchers to lend their reputation to support quality work.)