It's fairly obvious that was the case, going by the line at the end of Generations where he says he always thought he'd have a crack at the ENT-D Captain's chair
This is the most likely explanation. Riker probably reasoned that he'd be more likely to get the Enterprise
if he stayed aboard and allowed Picard to turn the ship over to him when he retired from Starfleet.
However, I'd really tend to think it wouldn't work that way. Why would they give you the flagship on your first command? What's more likely to expect is what Picard did with the Stargazer, & what he told Riker he should be doing when they offered the Aries. Get you a little ship & head out to the farthest reaches of space & relish in being the captain of your own ship carving into the universe
Riker may have been concerned that he wouldn't get another shot at the Enterprise
if he left the ship before Picard gave up of the vessel. What he didn't take into consideration is your point about being able to distinguish oneself by commanding another ship.
Picard wasn't simply given the Enterprise
. He earned it due to his outstanding service record aboard the Stargazer
. He was already a legendary figure before he commanded Enterprise
. Riker's status as the ship's executive officer earned him a great deal of noteriety and respect in the service, but the Enterprise
was never his ship. Even in Picard's absence, Riker was viewed merely as a place-holder until JLP returned. He would have been better served by taking a command like the Aries
and using that as a springboard to better command in the future. He certainly could have gotten another ship once the Aries'
voyage to Beta Omicron was over.