This is simple.

1. If you let them lie, then you have to correct them. They still get to spread their lie and some viewers will believe the liar, not the media.
2. Why should they stop lying if the networks will still have them as guests? The networks want to seem impartial but the division now is not between liberals and conservatives, it’s between people who tell the truth and people who lie. Sure, all politicians lie sometimes but you can’t compare the two parties now. About 2/3 of the Republican party believes that Biden didn’t win a fair election. As far as I am concerned, anyone who says this should never be on TV. The Big Lie is not an opinion, it’s a lie.
3. I am fine with people who have different opinions. I don’t want or expect everyone to agree with me. I am not fine with liars and bigots.
4. My mental state is better because I don’t watch the news. I was getting too angry every time Trump or his cult members were on. I can’t stand the sight or sound of him. He has done more harm to our country than anyone since the Civil War. I still keep up with the news by reading The Washington Post, The New York Times, and two local (Baltimore) papers. They have failings too but they’re better than the TV networks.
5. We have to remember that the networks are in it to make a profit and they had better ratings (and thus made more money) when Trump was president. Trump is awful but he’s great at drawing attention to himself. The media eagerly repeats his latest juvenile nicknames and spreads his online posts.