My thought is if TK won't plug Impact, won't have TNA talent on the show, then there's no reason to be doing this crossover other than letting Kenny do whatever he wants. All this relationship has been AEW making TNA looking even more second rate for really no reason other than they can. Even if Moose beats Kenny for the TNA belt, AEW most likely will just not mention it so it won't matter to anyone but people who were already watching Impact anyway. The only TNA talents to make it on AEW TV is Gallows and Anderson, and they're in exactly the same position as the goon squad to the actual talent they were with AJ in WWE that made them want to leave.
WCW, even when they did a WCW vs NJPW thing it was in a professional competition way, and WCW would always hype NJ as a huge promotion with super talented stars and then put them on TV and have them get 10-15 minutes on Nitro or a PPV and go over WCW talent even if the crowd had no idea who they were.
Well regardless of what belts they hold, or who they are aligned with, it's clear Gallows/Anderson have alot more creative input and having more fun, so that's where the win is for why you would leave WWE. Maybe same on screen scenario, but bet the environment is way better for them mentally.
As for the crossover, AEW was already running a feud with their own talents with Kenny, so that has to take priority over RIch Swann/Impact, on their own TV program. Is is Impact afterall, you don't shut down all angles to pull this "crossover" off. They did bring in Gallows/Anderson for the Bullet Club tease, which was an attempt to make something cool come out of the affiliation. And it tied into the AEW storyline with Young Bucks.
Impact really punked themselves, they should have never allowed the Tony and Tony "commercial" skits, it ruins the whole angle and buries your own product on your own TV show. Khan didn't pay for those, that was part of the Impact broadcast and it was part of creative that all parties agreed to and planned from the rip. It also allowed Khan to practice/establish an on-screen character while not plaguing his own show with "Diddy all up in the video" criticism.
I mean "our champ will come down and make appearances and carry your belt for awhile" seems like a short term positive. It wasn't "our champ will get your belt and will parade it on our main tv show on TNT", but still a positive. They just didn't plan the storyline well, pick the players well (Rich Swann should not be your heavyweight champ), and probably bent more to AEW's wishes than they should have.