Except we kinda do know what true extent of these realms are. The World of the Living represents our IRL universe made up of physical matter (Kishi), and then you have the Soul Society made up of spiritual matter (Reishi,which is stronger).
Kishi and Reishi can't mix, so when they travel to the SS, they are spiritual beings there, even the Quincies hiding in the shadows. This is probably the biggest reason why the World of the Living refers to the universe. Japan, Earth, Solar System, Milky Way, etc.
It would make no logical sense for the world of the living to be just a planet. The only realm you can argue is Hueco Mundo, since it's just supposed to be infinite sand, but we still don't know much of the origins of it.
For the story, we don't need to see other planets or even other countries. It takes place in Japan, the Seireitei, HM, and the Royal Palace. We're not going to see Saturn or Mars since the story doesn't need to involve them, but based on their statements we can come to a reasonable conclusion that the Living World is the entire universe.