The primary reason she didn't want the throne when she became Aes Sedai was because of her mission to locate Rand and prepare him for Tarmon Gai'don. She still may not want the throne, but this could have changed.

I have had this same theory for awhile now. If her and Thom get together - which seems very likely at this point - they would make an excellent royal couple, especially considering their aptitude for Daes Dae'mar. And, as was pointed out, Rand saying Elayne will be Queen of Cairhien as many times as he has is a good indicator that she won't be. Elayne is still preoccupied with Andor, and, even with Travelling, would likely have some difficulties managing such an expansive kingdom. Moiraine as queen gives her a role in the post-Tarmon Gai'don world that makes more sense than her becoming just another Aes Sedai.