#3 Lack of effective heels
I will make this statement before we get started. Chris Jericho is a legend. His title reign as the inaugural AEW Champion helped elevate the company and immediately made the title feel like an important championship to chase. Jericho's loss to Jon Moxley at Revoultion helped solidify Mox on the top of the food chain.
AEW certainly has various characters who are heels and are portrayed as such. Like many wrestling promotions nowadays, it is extraordinarily difficult for a heel to get the kind the heat that is expected. Nearly all top heels are unable to garner significant, continuous heat.
One of the best examples of this problem was with the first appearance of MJF on Dynamite after Full Gear. He had screwed Cody over by throwing in the towel, thus ending his championship match, resulting in Cody losing the chance to ever receive another shot at the AEW World Championship. His entrance to the ring reflected the results of his betrayal, as he arrived to a chorus of boos. Within a few minutes, however, the crowd had performed a 180 degree turn and was laughing along with him and "Le Champion" Chris Jericho. They were even outright cheering the two heels.
Similarly, Chris Jericho is one of the company's biggest bad guys, probably the absolute biggest. Even a legend like Jericho finds himself being cheered. His entrance always triggers a sing-along to his popular self-performed "Judas" theme song. This behavior is expected for a top babyface like Cody, but it is not expected for the man who should be hated for his words and actions.
This is not a fault on the part of the wrestlers or the booking. It is rather a drawback of having an audience which largely consists of hardcore wrestling fans who know a lot, maybe too much, about how the business functions. They appreciate the hard work that goes into creating a character and ultimately end up applauding the tactics of villains because of perfornances done well. Due to this, it is almost impossible to generate sustained heat.