Seems like some players will have instantly better accounts then others if only 30% of players get 2 legends and everyone else only get one. You would have to add the Legendary Birds for Kanto, Eon Duo for Hoenn, Lunar Duo for Sinnoh, and 3 musketeer Trio for Unova, and use the mechanic above to choose which one or even base it on the starter u choose so people can pick the legend that way(Duos could just be 50/50 shot). This way you can keep the king of the hill legends and everyone get at least 4 weaker legends to use for story. I would make it so u can only have 1 or 2 in your party at one time for balancing (Gym rematchs would be way too ez) and untradeable. Also, it is well know there is a Pokémon multi-verse, and that all players are within their own universe. Therefor, every legend really should be available to everyone, but for balancing purposes they aren't. All and all seems like a way to allow legends in the game without upsetting the balance.
Multi-verse explained: