Showdown is a poor measurement: the Monotype council, for example, has explicitly stated that all types should not be viable.
When it comes to balancing, there is no real way of achieving "true balance", meaning all types, characters or whatever it is that's competing against one another, would be equal in power or viability - especially in regards of competitive play. With that said, I believe there is some degree of bias in terms of Pokemon design: quite a lot of Legendary and Mythical mons are either Psychic or Dragon-type. I don't know for sure how often typings stem from whatever inspired the design: for example, Solgaleo could be based on the lion that eats the sun, which in turn is related to alchemy. With this point of view in mind, one can ask how much sense it would make for Solgaleo to be part Fire-type - or Steel, which it actually is.