It's good to remember that the previous American president also waged a war against every media outlet he didn't like by claiming they were "fake news." It's the same authoritarianism in different stages. And if you think nobody in America wants to jail journalists and media CEOs, go look at any forum with a substantial amount of Republicans talking freely.
Or for a more concrete example, look at how both Republicans and Democrats are treating Julian Assange. Investigative journalism and whistleblowing are under attack by all political factions and by the justice system, today. We cannot treat anti-free-press authoritarianism in the West as an "early stage" or tomorrow's problem.
But yes, we need to take it extremely seriously in the West and fight against any and all encroachments so that we don't slide further towards authoritarianism. Recent trends have been concerning.