I think the best way to think about it is the cast for Season 1 was explicitly created for Season 1 - or at least whatever rough draft of Season 1 they originally intended. Clearly in some cases (like Elnor) they already really cut back on what they intended by the time it aired.
They were already struggling to find excuses to have Picard's band of misfits together for Season 2...though I don't know why they didn't just pick up where Season 1 had left off, with them as a ragtag crew of La Sirena. Still, once they parted ways, there was really no reason to presume they'd all be thrown together. And Soji and Elnor played essentially no role in Season 2 anyway.
I have no inside knowledge, but it sure seems as a viewer that Rios may have been destined for the past from early on. The record player. Billie Holiday. Love of cigars. And the fact that he was ostensibly miserable. Maybe the writers took that & ran with it, but there were S1 hints he is a 21st century guy. Once I saw Teresa, I knew he was staying.
Ditto with Jurati. Another tortured lonely soul from jump. Who never fits in. She murders her ex-lover. She is fascinated by artificial intelligence. She is tormented. Her & Rios don't really work. Early in S2 she is also miserable. Again, maybe than just ran with what was there already, but therexare string S1 hints.
Again, the show is called Picard. Not Soji. It is about HIM. Not THEM.
S1 is about his present. His health. His issues about the Romulan rescue & leaving Starfleet. And Data's death.
S2 is about his past. His relectance to form attachments. It literally takes place in the past, just to reinforce the concept.
S3 is about his future. Where does the now retro-fitted Picard want from here.
While I admit the thought of Picard, Soji, Rios, Elnor, Seven, & Raffi bouncing about on La Sirena has some appeal, it is not true to the characters. Soji needs to be an ambassador for her people. Jurati is a scientist. Picard's cause is over for Elnor, he needs another. Ex-B's? Seven needs to decide how to proceed. And there is no natural partner for Picard 9n the ship. They accomplished the mission they signed on for.