To add to Steevy's post: traditional over-the-air stations/channels remain separate from the networks they pull content from, and despite a glut of content they could be pushing, network feeds still have limited hours of operation leaving space (afternoons, often all day Sunday, overnight) for local or cheaply sourced programming, and I'm pretty sure this is by FCC mandate, to ensure people have a way to watch the local news, weather forecast, and free coverage of local sportsball games. Cable-only channels, however, operate a 24/7 feed relayed directly by the cable companies. If there were ever a conflict between a cable company and a particular channel's content, their only recourse would be to drop the entire channel from their lineup, possibly along with every other channel owned by the same media company. This has happened before, with one of the major cable providers (Cox, maybe?) threatening to drop MTV, VH1, Nickelodeon, and a few others over a dispute with Viacom. Also there's PBS, which doesn't provide a feed at all; they just have a bunch of content and the stations have to pick and choose what to air and build their own broadcast schedules.
Over-the-air TV still exists, despite occasional efforts from cable providers to persuade the FCC to shut it down. Due to former FCC limits on how many stations one company can own, most stations are not owned by the same companies as their affiliate networks.
Wikipedia has a list of current and former exceptions; you'll notice that ABC has the fewest of any of them. Even under the much more lax current regulations, no company can own enough channels to provide coverage to more than 40% of the country, so it would be impossible for a network with nationwide coverage to own all of its affiliates. And no one wants to own a station that runs content from a rival network. So what's happened is that we've seen a rise in "station swallowers" like Sinclair that don't care whose affiliates they buy; they just want as many eyeballs as possible watching their politically-slanted national news stories being read word-for-word by hundreds of "local news" anchors across the country, as John Oliver explains below: