How in-house does it need to be? The actual physical facilities aren't being shut down; they're just under new ownership and management. And Nippon Steel is located in Japan, which is such a dependable ally of the US that I'm politely trying not to use the phrase "vassal state."
Also in the US, we've got Steel Dynamics (producing 75% as much as US Steel), Cleveland-Cliffs (approximately tied with US Steel), and Nucor (about 157% as much). That's not the whole story, of course -- Nucor primarily recycles scrap steel, for example, as opposed to smelting ore -- but I'm not really seeing a crisis anywhere on the horizon here. (My opinion in this paragraph is less confident than the first, so I'm open to correction from someone who knows more about the steel industry.)