I do think most of her support within the show came from the other attempts at giving Sonny love interests flopping (Angel, before that, Hannah), or Guza just not wanting to actually write them as a real long-term pairing (Sonny/Alexis). Tamara Braun did win viewers over, but it didn't really matter, as the show was always going to put Sonny first (as shown with him being the sympathetic party after accidentally shooting her in the head while she was in labor).
By the time Laura Wright came in, the canvas was thin enough to where they had to make Carly even more of a central figure. I would say Laura is also more naturally prone to sympathetic portrayals than someone like Sarah Brown, although she's still a somewhat cold actress, which suits Carly more than the writing itself does.
Definitely. That's one of the reasons I'm surprised they even actually paired Spencer and Trina in the first place. As you said, I imagine Joss and Dex were, and are, the main goal.