Here's a reasonable explanation: If you're the world champion, then you're the "face of the company", at least for as long as you hold the championship. If Wyatt is "the face of the company", then that provides him with the best possible platform to spread his message to the WWE Universe, it means it's his face plastered on all the posters and advertisements for WWE events and products. Is this not exactly what Wyatt wants? For everyone to flock towards him en masse and embrace his way of thinking? That seems to be as good a reason as any for wanting to become the champion. And it's almost completely identical to why he targeted John Cena, because he realized Cena was that guy that everyone (well, most everyone) looked to and followed as a role model. He wanted to take apart people's perception of Cena and replace it with his own. Wanting to become world champion is a huge step towards becoming the face of the company, which would be striving to obtain the same exact goal, only on a much larger scale than before.
That's as logical reason as any as for why he would always want to become champion. And it's wrestling, so it doesn't have to be profoundly deep or anything (although that is pretty deep for the Wyatt character.) It would be akin to a Jim Jones-like cult leader wanting to become the President so that he could sway the entire public into his brainwashed way of thinking (reminds me of part of the plot of Resident Evil 4 lol.) Wyatt is a huge character and performer that they're investing heavily in for the future, they can't have him not challenge for the world title at some point.
