Pro tip: At some point, every president thinks this thought. Bastards.
The difference between President Trump and the others is that they don't think it would be wise to say so publicly - either because they think it will cost them politically or because they genuinely don't want to erode the public's trust in the free press. Trump doesn't care, nor should he. When an entire industry uses its megaphone as irresponsibly as this one does, they're doing great harm to the nation. They should be called out.
And according to a poll conducted by the Center for Politics, Trump voters didn't vote for him in spite of his belief that the press are "the enemy of the American people." They agree with him: