"I only have eyes for Nagi".... I don't think I have to say anything. The first two comments already said everything that needs to be said.
That aside, the whole "everyone is their own protagonist" thing is an interesting take, but what happens in a world where everyone is a protagonist? You can be great, but won't there be many moments where you'll have to be a supporting character, even if only for a second? You can't do it all, they are playing a team based game after all.
(If I missed something, which I probably did, it'll be better if you just let me know so I don't just embarrass myself).