I've hired (low) dozens of people in public sector environments, and neither myself nor anyone on my hiring panels has ever cared if we receive a post-interview thank you. Maybe private sector is different, but I'd just as soon not have you clog up my inbox with thanks or make a post-interview pitch about your skills/excitement.

If you say thanks in the room, we're square. Likewise, I always thank people for their interest and time in the role.