That's a good point. They make it fairly obvious at some points. It's unhealthy that they don't have him interacting with people that are older then him and that also outrank him though. They should have the full range of interactions possible. Is there even one episode where Picard interacts with someone who is older and also outranks him, which can only be an admiral? Or even who is the same age and is the same rank? I don't recall any.
Two characters that were older than him were Boothby from The First Duty and Professor Galen from The Chase. They weren't admirals, but they were mentors to him.