[WARNING: MAY CONTAIN SPOILERS]
Note: Okay, I have not read the light novels—I've only listened to the songs with PVs and read up to chapter 20 for the manga. Also, I have not read much theories, so everything here is an original. Any similar theories are completely coincidental. With that, here is my theory. It might be a stretch.
So, in Ayano's Theory of Happiness, the whole first half (?) of the song is basically on a TV, right? But then it zooms out and we see Ayano hugging it legitly. She was focusing on the past. She was watching her past and her fellow adoptive (?) siblings Kido, Kano, and Seto. There's not exactly really strong stuff in here, but it's a nice thing to note.
In Shounen Brave's PV, you can also see a TV. Seto is by it, and then he flashbacks to the past, seeing Little Seto.
Now, a thought just occurred to me while typing this up on my phone—when we watch our favorite shows on TV, the people who work there are actors, right?
In the Outer Science PV, we see Kuroha sitting on a pile of dead TVs. I thought (after watching the PV a gazillion times) that it reminded me of the time loop—it happened on for a long time. Each TV represented each past; each route that was reset. And Kuroha was sitting on top of them like a King, as if he was the cause for the many resets. And he was prepared to get Mary reset the timeline again.
Also, in Jubyphonic's lyrics for Outer Science (and yes, I know they differ from the actual translation), one of the lines was "reset the actors on stage". That really got the ball rolling for me. The people who were featured in the TVs were the Mekakushi Dan. The first word was also strikingly similar with the first word in a KagePro album name titled Mekakucity Actors. Let's focus on the key word: Actor. Remember somewhere in this theory that I mentioned that the people on TV were actors? What if the Mekakushi Dan were considered actors, since they were featured in TVs?
So, does that mean that each TV represents each timeline, or something?
These were just my thoughts on the whole TV thing. It probably makes no sense, since I rushed while typing this up, and was really excited for it. I'm sorry if it's all over the place, too.
Does anyone want to share thoughts and ideas on the TVs? Don't be afraid!