The U.S.S. Stargazer, NCC-82893, played an important role in Star Trek: Picard Season 2. It served as a nice piece of nostalgia that hearkened back to Picard's younger days. Then, for Season 3, they decided to introduce a ship with a blatantly anachronistic structure--the Neo-Constitution (the window pattern on the saucer is the exact same as on the Constitution, despite different ship sizes, and the saucer itself is from a design that is 150 years old). The new Stargazer follows the design flow of the era much better. What was the out-of-universe reason that they left the Stargazer and decided to go to the Titan-A? Did they consider using the Stargazer as the hero ship for Season 3?
Per showrunner Terry Matalas himself (video below), the goal was to create tension by putting Riker back on the Titan-A, when he had been captain of the original USS Titan. Transcript below from video captioning
We knew we wanted a starship adventure this season. The question is what ship? And when we tied into the story, and we knew Riker was going to help Picard sort of con his way onto a starship, we looked at his previous command. And what would be a really good conflict there, was to put Riker back onto the Titan. This sort of new starship.
Brian Tatoski added
With the Titan, it's an established ship, it's an iconic ship, but Terry wanted to sort of bring it forward to the next generation with also his own spin on it, his own take on it.
The best explanation here is that Picard Season 3 revolves around familiar Trek. You literally have an episode where the characters geek out at historic Trek ships in the museum. While the name Titan may not be as well-known to long-time Trek fans, it has played prominently in the Lower Decks series, and has its roots in broader canon. Clearly Riker has made a name for himself and that ship on its own. The Stargazer, however, was purely a name throwback to Picard's original command, and was only shown briefly in two episodes total. Since Rios is gone, there's no real reason to revisit it.