It's chicken and egg, really. Somehow, they found out he became popular and they started pushing him. But it wasn't a forceful "Till Death" push, where no one was biting. Abby almost was, unlike Elmo. I once had a writing teacher tell me that kids specifically like 2 kinds of characters over all others. Goofy, childish ones, and actual children they can relate to. While there are other characters to relate to, Elmo's the most generic of the group, personality wise (i.e. not neurotic, grouchy, overly eager...etc.) not to mention he's the same age as the target demo. Then again, Elmo's stardom, while it started to climb in the early 90's, came out of the necessity to fill out a cast that was left decimated by performers passing on or moving on (well before they recast major roles) and other new characters failing to stick or relate to kids. Elmo may be pushed a little, but he stuck while characters like Benny Rabbit, Sherri Netherland, and the Monkey Brothers quickly ran out of material, and thus lost their relevance.
However, I've noticed that Sesame Street is marketing and using the core characters. Ones that stood the test of time that have always been on the show. Ernie, Bert, Big Bird, Snuffy, The Count... etc. Just no Mumford, Placido Flamingo, Sam the Robot type characters. Unless it's something specifically nostalgic.
That said, whatever season is filmed after the one currently in production is going to be interesting with a recast Elmo. If his role is diminished a little, leaving room for other characters, that would be the only positive thing coming out of that. But then again, there's going to be gaps if Muppet projects conflict with SS's taping.