If you seriously think that people in the federal government don't try to control the media narrative, you're ignoring a huge body of history where they have done exactly that.
I'm not trying to debate the rightness or wrongness of Alex Berenson, I'm simply pointing to this as an example of the federal government strong-arming corporations into censoring people. Alex Berenson might be someone you disagree with, but remember, tomorrow there might be someone in power you dislike and they may choose to use the power to silence people you do agree with.
When you give someone a gun, especially someone powerful, especially the federal government, you can not predict who will be holding it in the future and where they will aim it.
How much strong-arming is going on vs. active reverse lobbying. We see real censorship (backed with guns) in Russia today -- I don't think this is comparable to the current administration asking CEOs to not enable the spreading of verifiable misinformation.
I find it interesting that other bans don't get the same concern from the usual suspects, e.g., abortion gag laws, library book bans, don't say gay laws, etc.
Should the former president retake office I expect bans of political enemies and more -- the type of abuse that you rightfully fear.
This is a nuanced subject and requires corresponding consideration. We all agree that some speech isn't good for society but remain at odds over what that speech is.
I can understand why the WH was concerned.