This is one occasion where I get both sides of it so to speak.
Gresham's point: He is, in terms of technical wrestling, probably top 10 in the world and that is a conservative estimate. While ROH was suffering, Gresham was one of the guys who at least tried to keep it going. The Pure title tournament for the title's return was something which actually did bring some eyes to the product again, at least for a small time, and Gresham was a big part of it. Also, as ROH Champion, he should have had more time to introduce himself and showcase himself to the AEW audience. Show the world his strengths. He's an asset and even if you don't want him as the champion forever, present him as something to be hyped about and it means more when someone beats him. Losing to a new signee quickly sucks, especially when it is the classic "Ex-WWE guy wins title" at face value. Gresham is good, and even if using your PWI rating as an argument is a touch... cringe, I get the point. From the time AEW got back on the road, there have been concerns around communication.
Counter points: Wrestling is still a business. I will not knock Gresham for his size because he is still a beefy beefy guy who can lift people larger him and tie them in knots, and MMA has shown that people of different "weight classes" can be big draws. With that in mind, Claudio is the still the better person to build ROH around right now and give it a jolt. Claudio is a bigger name, he is still an ex-ROH guy so he really stands for the ROH's bedrock and can act as a bridge between old ROH, current, and new. He is also more well rounded than Gresham. Even if Claudio is not a master of the microphone, he still is competent on the mic has a physical charisma, and can wrestle plenty of different styles, power, technical, athletic, etc. Gresham is someone who even in his 30's still has room to get better, but he isn't where Claudio is right now. Also without TV for ROH, it is hard to find time to put him in the middle of all your stuff for AEW when you are also building your other PPVs like Double or Nothing and Forbidden Door.
So to conclude: I think Jonathan Gresham has valid concerns and criticisms. No matter what happens with him, he stays or go, AEW has a chance to hear these concerns and work towards improving things behind the scenes. But, if his main concern is not being ROH Champ (doubt it is only about it, but may be the biggest thing), then I'm sorry, dude, but even with getting a raw deal, Claudio is the better person as champ right now and you can still find yourself in the hunt for it again, or ROH's other belts, or in AEW.