Unfortunately, it will be an uphill battle getting the major cable companies to support this. The whole point of "TV Everywhere," from the cable companies' point of view, is to make it a massive pain in the ass. Every Apple TV that uses TV Everywhere to watch video is one less cable-box rental fee, and one more person who is a step closer to cutting the cord entirely. It's not in their interests to make it easier for you to use TV Everywhere.
Consider: You need to go through the annoying log-in process even to watch broadcast networks. Anyone can watch the show by using an antenna, but if you want to watch it online, you need a cable subscription. Theoretically, those networks are supported by ads. The live streams and replays in the app have at least as many ads as the terrestrial broadcast—sometimes more. But you still need to pay for a cable subscription to see them online. And that means the cable company has to pay the broadcaster retransmission fees for carriage.
This is why the "true" Apple TV never happened. The TV networks and cable companies have no interest in working with Apple: Apple wants to make it easy for people to watch TV, and the TV folks want to make it hard for people to watch TV without paying a lot of money and using cable-company equipment that can readily monetize their viewing habits.