See, back when I was involved in print publications, "masthead" had a very specific meaning. It referred to the box of text that contained the title of the publication followed by a list of the people involved in producing it, including editorial, sales, circulation, and subscription staff, as well as any relevant company/corporate information. It would appear on the contents page, or the letters page, or somewhere else close to the inside front cover.
Sometimes people, usually designers, also used the term "masthead" to refer to the stylised text of the publication's title that appeared on the cover or, in the case of a newspaper, at the top of the front page.
But nobody ever used it as a synonym for the publication itself. If that's what you mean, why not say, "this publication" or "this newspaper"? Why take something with a very specific meaning and try to give it a generic meaning?
Somewhere along the line, some dickhead used it because he or she thought it sounded fancy. And other lazy dickheads copied it for the same reason. And now it's "this masthead" this and "this masthead" that. And yes, it annoys the **** out of me, but so does much of the world as we have come to accept and know it🙂