Seems false. The Atlantic Monthly, to take an example --- another publication I subscribe to --- is an order of magnitude smaller than the Post. If the Post wanted to run the Atlantic's business successfully, they could; they'd just have to lay almost everybody else in the company off.
That the Post's predicament is a consequence of Bezos partisan editorial decisions. I don't like those decisions either, but I don't think they get close to the core problem the Post faces.