Nexstar drew national attention in September after Disney, the owner of ABC, suspended Jimmy Kimmel’s late-night show because of on-air remarks that the comedian had made about the Trump administration’s response to the killing of the conservative activist Charlie Kirk. When the nearly weeklong suspension ended, Nexstar, which owns dozens of ABC stations, continued to pre-empt the show with other programming for another week, effectively preventing it from airing in large parts of the country.