The Mandate tutor many, many students, primarily the sons of wealthy, powerful men. The powerful and wealthy have sons who are heirs. Proyas is not special in that regard.
What makes a man need truth? Kellhus demonstrates over and over that All men desire truth, its how me controls. He explicitly says that small truths make men belive. Proyas, again, is not special.
And what of Judgement? I presume you mean that in a religious context. But we are told that Kings with multiple heirs send their younger sons into the Thousand Temples. Lots of them, I'm sure, end up with a powerful need for judgement and faith. So, again and again, Proyas is just a Man.
Further, how many sons went on the Crusade? Many, many powerful households sent not just one son, but their entire lines. The Conriya house was not unique.
Nothing about Proyas is special, except that Kellhus chose him. He could have chosen any son from any of the neumerous powerful houses in the holy war.