I usually get the thank you when they want to bring me to the next round of the hiring process. Maybe the thank you acts as a kind of signal that a party is interested in keeping the process moving? I’m sending a follow-up email if I’m eager to keep things moving (and it’s not simply “thank you for the interview;” I’m including a couple brief points reiterating why I think I’m a good fit). If I’m ambivalent or not interested I wouldn’t put the effort in.