Moxley is booked about the same as he was in WWE in 2016-2017 or so. He always wins, he's over, but is also prone to getting involved in some silly shyt and lacks the aura of irreplaceable star that he should have, especially in a start up like AEW filled of mostly talent with little mainstream national wrestling exposure.
He's a guy who had Undertaker's last TV singles match, had a Wrestlemania feud with Brock Lesnar, was part of the most dominant faction in years in WWE, had SO much TV time over the past 7 years, and yet he could be replaced with just about any about anyone on the AEW roster after the PPV and nothing would change. Swap him out with any member of the Elite, Darby, Scorpio, PAC, etc. Actually I'd argue that even with some questionable booking themselves (especially Omega), both Cody and Omega both feel like bigger stars than Moxley. Which really shouldn't be the case but that's how it feels.