During an appearance on 'Rasslin w/ Brandon F. Walker, Bryan Danielson explained why he hasn't been doing the "Yes!" chants in AEW: it was actually a request of WWE before he debuted.

“So I had a great conversation with Kevin Dunn with WWE before I debuted with AEW. I was very upfront with WWE about, ‘Okay, I want to let you guys know I’m leaving. This is my debut date’ and all that kind of stuff. They asked me, politely, to respect their intellectual property, even some of the things that couldn’t be legally enforced. I’m trying my best to do that.”

Danielson visibly nods his head along with the fans when they do it, but doesn't engage himself in the chants.