"without his unearned power" is an important part of that sentence
It explains why liberals care what he says. I would suggest that his unearned power is not because of his wealth and privilege, but because he is an established fixture in the RW echo chamber. If for some reason, his power is ended, it may not help because another replacement "cog" in the RM media machine would take his place.
It is easy sitting in a liberal bubble - Burlington VT - or even former Republican stronghold Morris County, NJ to consider that these people and their outlandish ideas should be inconsequential, but they aren't. I just returned from driving to and from Northern Indiana where we saw my parents for the first time since the pandemic started. For most of the drive, we listened to podcasts or music, but on the return trip, we regularly searched the dial for information on the George Floyd trial when we were driving through rural areas desperately in need of internet service! What we found was mostly rw talk radio, Christian stations - many with a bizarre political version of religion.
My family in Lake County Indiana is reliably liberal/Democratic. A sister who had returned from the West coast to help support our parents spoke of how weird looking for a church there has been. Religion is important to her. At first I thought she was speaking of trying to choose while viewing them remotely due to covid, but she explained that many of the churches had decidedly right wing views and values she never thought a Christian church would accept.
The power that people like Carlson have is that they have a platform to spew hateful ideas, that ALL the right wing talk people seem to simultaneously, but in different ways, spew. This is the very definition of an echo chamber. Back in the early 1960s, I remember a teacher suggesting the way to form an opinion is to read multiple newspapers. I suspect that since the 1990s, many people THOUGHT they were doing a version of listening to multiple sources, when in fact, the various voices on the right were validating each other. Now, it may be even worse as, for many, it is not just the "news", but their religious leader, who they trust is on board with the same distortions.
Back in the 1960s, while the Chicago Tribune and the NYT rarely agreed in the editorials, the news articles, while sometimes emphasizing different things, at least described the same world -- and most people trusted Walter Cronkite. Now, there are two - or perhaps more, realities through which everything is filtered. So many people have spoken about how we need the same "facts" before we can even start to return to a less polarized country. What I can't imagine is how we can move in that direction.