Your first sentence is incorrect. Monopolies are not illegal.
From the press conference this morning: "It is not illegal to hold a monopoly, Garland said. "
"That may sound counterintuitive in a case intended to fight monopolies. But under US antitrust law, it is only illegal when a monopolist resorts to anticompetitive tactics, or harms competition, in an effort to maintain that monopoly."
https://www.cnn.com/business/live-news/doj-apple-antitrust-l...