#1. Doesn't want to go - AJ Styles
AJ Styles revealed in a recent interview that the recent WWE contract he signed was "definitely going to be his last". Now, the time period wasn't specified, but the general assumption going around is that the contract is no more than 2 or 3 years.
That's a fair deal and we're sure that AJ Styles is getting well paid for that period of time. Like Shinsuke Nakamura, WWE is basically Styles' retirement fund. While he's made great money outside of WWE, he's been wildly successful in the past three years, becoming a bonafide top star and a 2-time WWE Champion.
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There's little doubt that his success will continue and while he most likely hopes for AEW's success, there's really no incentive for him to go to the promotion. He has nothing left to prove and the PG environment of WWE draws Styles in more because he's a traditional family man.