Players know that all types will occur with the same frequency and I doubt that there will be a mass flocking to one or two types. Especially playing among friends. There's also that you cant colonize planets in other empires, meaning that the nearby habitable worlds to another species may encompass the tundra world you want, or make it difficult to colonize it.
immigration - though the ais wouldn't configure their laws to allow it to happen), and it's likely players would use the same tactics. Not to mention how inter-player deals are literally always the decider of borders, and would be a super-easy way to spread species around.