The only problem with this is that the population in the Caralain Grass and Black Hills is sparse and neither country has much in the way of excess resources to try and impose their will. Both Andor and Cairhien have claimed the empty lands north of their current borders, but they've pulled back because they weren't able to hold it. The world of Men is failing, on the virge of the Dark One's escape from his prison. True peace from the Shadow and time to grow is the only way to become vitalized (and populous enough) to think about claiming the abandoned lands of failed nations.

Elayne taking control of Cairhien is different: the nobles and people there are willing to accept her, so she isn't required to do very much in the way of forcefully holding territory. I think it safe to say that the two nations will eventually become one in time, and called Avalon (per some of the chapter headings early in the series).