OP mentioned "the most popular news outlets". I expect that there's pretty good intersubjective agreement about which entities are in or out.
It's true in one sense that there's no such thing as "the media". If "the media" is just "the set of people who write things about current events that other people read", then I, too, am a member of the media. Groovy.
But this is an isolated demand for rigor. If you look at who's employed by "the most popular news outlets" (which can be relatively objectively determined through subscription numbers), you cannot help but notice that they are a rather distinct class. They come from particular schools, live in particular cities, have particular points of view including suppositions so basic that they often do not even realize that they hold them, understand themselves to be accomplishing particular professional and social objectives through their work, and so on and so on. None of these qualifications are strictly categorical, but as a statistical matter they are so robust as to be tedious. Which is all fine, so far as it goes, but the concept of "the media" is "a thing" inasmuch as it allows you to concisely name patterns and regularities that exist in the world. And there are an awful lot of patterns and regularities to be noticed.
Incidentally, Orwell made precisely the same point (about a distributed, decentralized press that coordinates through shared cultural background and sense of what's simply Not Done) in a proposed preface to the first edition of Animal Farm. The free, decentralized, totally-not-a-thing British media declined to print it.