America just had a President who explicitly declared the press to be the enemy of the people.

Ignoring the degree to which the American press voluntarily acts as a propaganda platform[0], the US government absolutely does censor the press, by revoking or controlling press credentials, arresting reporters covering protests, harassment, etc[1].

And the US has historically censored the mail, yes, usually during wartime. But the bigger problem is surveillance - the USPS tracks, photographs and logs all paper mail for government surveillance and law enforcement[2]. The USPS also has a 'covert operations' division that monitors social media posts[3].

You could (correctly) claim that this isn't nearly as bad as the surveillance and censorship regimes elsewhere, but it's difficult to see how making that easier by giving the government direct control over a primary means of global communication makes it less likely.

[0]https://www.thoughtco.com/how-media-censorship-affects-the-n...

[1]https://fair.org/home/us-censorship-is-increasingly-official...

[2]https://www.nytimes.com/2013/07/04/us/monitoring-of-snail-ma...

[3]https://www.salon.com/2021/04/21/is-the-post-office-spying-o...

In living memory, through McCarthyism.

I guess that depends if you consider WikiLeaks part of the press.

During the Trump administration, their vindictive treatment of the press and the selective removal of access to the White House by outlets not toeing the line more or less amounted to quasi-censorship in practice.