It's like being on Earth, in modern Flame Nation, bearing the last name of Li, and claiming your ancestors were Emperor Taizong of Tang Dynasty. You attempt to show a heap of genealogy records, family emblems, and other documents to validate your claim. But does it make any difference? None whatsoever in my Roberts Kingdom.
Even if you were descendants of the emperor, it's impossible for you to be given an emperor's throne in modern times. Hence, it might seem impressive to say, but it serves no real purpose; this is likely the case with the Nine-Star royal family. Finn Lewis was mistaken thinking there'd be some pleasant surprise.
Currently, aside from obtaining the Solar System, there's not much you can gain. And in truth, obtaining the Solar System doesn't provide much advantage as it's just an ordinary planetary system. It's not because Finn Lewis feels indifferent to such acquisition.