It's pretty established that Starris is a perfect world at this point, right? No hunger, no death, no problems.
But without any of those things... what else is there? If there's no problems to be solved, then there's no need for jobs outside of a select few. Everyone is likely on equal ground in terms of class as well, since there's little need for money anymore. It's recreational at best, since its not like anyone needs to eat.
While this may sound like a utopia at the surface, is it really? Wouldn't a life with no challenges become monotonous after a while? Wouldn't each day blur together as you fall into the same understimulating routine?
Sure, many people would be satisfied with that, but not the Regent. Not a man who's response to defeat was not giving up, but to keep going, to try harder, to return again and again to the Architect despite dying every time. He seeks not just to survive here, but to become Preon's hero. His ambition (and arrogance) is boundless; too large for anything on Starris to satisfy.
And consider what he actually does in battle. One main category in his full collection of cards aside from magic is smithing. There's multiple cards that show him smithing and polishing his swords by hand. Swords that would have had no use in a planet with no conflict. And what use is a sword otherwise?
For all his pomp and snobbishness, the Regent is determined. He adores challenge and the subsequent victory, he adores showing off and becoming better and better each time. For a spoiled prince, he's very persistent, and willing to get his hands dirty if it means he'll emerge victorious.
That's why his presumably final words to the other Starrians is "You are BORING!" because if he stayed, it very much would be.
Perhaps there's also some part of him that just needs to be needed. After what was probably a good chunk of his life being prepared for when his people need him, only to just... not be needed anymore. The only thing he can think of to do is to find somewhere that does.
He doesn't want to end up as a sword decorating a wall; a deadly sharp edge confined to a frame, its only purpose being to look pretty or to look intimidating with no substance behind it.