Live TV integration is something that the 360 has (in a limited regard; only a few channels), but unless I'm mistaken, the One is going to function as a fully featured set-top box (all channels, integrated guide with search, voice commands, etc.). The software features seem like they'll be more robust than what the cable or fiber company can provide on their proprietary set-top boxes. I know that I personally find Verizon's set-top box software to be clunky.
Things like interface and usability for media features matter to a lot of people. When I still lived with my parents, they would use my 360 as their DVD and Netflix player, and my father often made comments about how he preferred the 360's interface to the PS3's interface. It made a difference to him, and to my mom, who's not really a technical person.
That doesn't mean that the 360 is completely perfect; you can always make improvements to user interface by getting feedback from users and streamlining things. That's what Microsoft is trying to do with Xbox One, and from what I saw from their presentation, the upgraded hardware improves the user experience. That matters.
You're conflating two arguments incorrectly. The all-in-one device analogy was brought up in response to people taking issue with games consoles in general doing more than just playing games, not in response to what Microsoft specifically did at their press conference.
The preference of consumers towards all-in-one devices is a justification/explanation of Microsoft's overall strategy with the Xbox One, not of their press conference presentation content. Like I said before, Microsoft is planning on focusing on games during E3, which is a few weeks away, and arguably a better place to talk about games content anyway.