Indeed it seems illogical.
And note that there's also Epoch. Three of them could go through the gate with the Gate Key, while three others could ride the Epoch to time-travel to wherever-whenever they pleased. Meanwhile, someone would stay behind in that case. Probably Magus, since he's so antisocial and nobody actually loves him. Except for Lucca.
But I see this three people only thing, including Gaspar's statement, as a resource to make a more organized game. Imagine how it would be to control all 7 characters at once. A lot of fun, I guess, but it might not work as well as actual battle system with 3 characters does. Too many variables, too many options and too many characters on the screen would probably annoy many players. Even while just walking or on world maps, it might not feel good for players to have so many characters on the screen. I think a "cleaner" screen would be preferable.
My conclusion: If it wasn't a videogame (I mean, a book, a comic, a series, an ancient tale engraved in stone), everybody would be capable of going everywhere and at every time together. And that includes Magus tightly holding Lucca in lovely hugs and hot kisses.