The FCC, like other federal agencies, is independent. There's nothing in the article to suggest that Carr's decision to do this has anything to do with Trump, who doesn't actually have authority here. Per the article, Carr apparently doesn't think he did anything coercive either. He's just making public statements. The supposed "threat" doesn't seem to me like much of one.
And Carr is also irrelevant to the Kimmel firing. ABC faced pressure from affiliates and his ratings had been declining for a long time.
Trump does not share your view that they are an independent agency.
Carr also does not appear share your extremely charitable interpretation of his actions. He has subsequently confirmed that he sees this in line with the administration's larger political mission and is being about as subtle as a fog horn about his status as a political hatchet man:
And Carr is also irrelevant to the Kimmel firing. ABC faced pressure from affiliates and his ratings had been declining for a long time.