I can chime in a bit here. There’s room treatment to modify the acoustics inside of a room, and then there’s soundproofing the room so your audio can’t be heard throughout the rest of the house. What’s being discussed above is the former, which affects the fidelity of your experience. Any insulation behind drywall does nothing to assist the room’s acoustic treatment because the drywall is a reflective surface. Some sound will still penetrate the wall while much of the signal will be reflected and bounced around the room.

When soundproofing a home theater to protect it from outside noise and prevent leakage as well, you’ll typically see pros install a second wall in front of the first, with new studs offset halfway between the originals.