Really he'd probably be a lieutenant commander or commander by that time and head of "Astrophysics" or whatever sub department he's in. He'd still be reporting to someone else, probably Data or an unnamed Chief Science officer, even if he nominally outranked them.
OTOH, Starfleet not having an "up and out" system like the military makes sense too. Academia often promotes younger more ambitious folk over older but more experienced ones. Picard as the guy who does math nobody likes could just be his thing.
It's also possible this Picard refused promotion (or didn't pursue it) until he'd been replaced by "Real" Picard. Then, to Deana and Riker, it comes off like a midlife crisis than actual ambition.