The server limitations exist because once you hit a critical mass of people in an area, the performance of the game nosedives. On Friday, when I first entered the Sea of Clouds, my FPS dropped down considerably and people experienced crashes because there were a thousand characters hovering around the aetheryte. They already increased the concurrent login capacity shortly after 2.0 launch, putting most servers around 8000 characters online together maximum.
That said, the login issues over the weekend were part server capacity, part lobby server capacity. The lobby servers have to juggle the queues for all the actual game servers, and the queues for Balmung and Gilgamesh overwhelmed it. If anything, the lobby servers need to be re-jiggered to handle the loads better, or we need a third data center (e.g. lobby server + server cluster) in NA to split Balmung and Gilgamesh apart. (Primal's lobby server is also straining under the load, but it's not buckling like Aether did.)