Yeah I think all those characters do choose to have their companion pokémon/their aces. As such, the MC/the player also can choose to have an important pokémon who doesn't leave the team, (or choose not to have it, lol). I had a shiny Medicham in the team since the first adventure with Melia, and along with a few more, will probably be from v13 on. I don't really like the idea to force a pokémon on the Main Character, like yeah as a symbol (like on Insurgence the main gang are chosen by a mythic pokémon) do what you want but I choose what pokémon goes with me, thank you very much.
Plus, yeah, I'm not against linking any character to a legendary/idea, like the Regis/protectors, Dialga/Palkia/Giratina and the three sisters, Melia and Arceus/Xerneas... I go with that other comment saying the Main Character would be linked to Zygarde. But I don't think this is about symbol pokémon.