Unlike Trump, who needs the MSM to serve as a foil, Richard Nixon genuinely hated left-wing media figures. He used all of the powers at his disposal to bring them to heel. But he was never in a position to legislate their rights away, and the judicial system was there as a backstop against First Amendment rights violations. The danger he presented to free speech was, therefore, pretty limited.
DeSantis appears to have roughly the same level of animosity towards any media that lean to the left of Fox News. Unlike Nixon, he has shown that he can push legislation restricting the rights of media companies through the system, and he has a friendly judiciary standing behind him. Would the First Amendment rights of blue people be protected if he is elected president? You would be a fool to assume so.