The servers are designed to handle 5000 people concurrently - spread across the server. They know going into this that the 3 start zones, Gridania, UlDah and Limsa are going to be the initial pressure points with far more users than any other, so I would think that the zones themselves are capable of holding more than 1000 simultaneous users. However on opening day, imagine if the server tried to allow all 5000 concurrent sessions into these three zones alone, it would collapse. Which is why they were initially throttling logins.
Limiting logins and the creation of new characters on servers is necessary at the start because the majority of players are packed into a small number of zones within the game. To make the game playable, you actually have to put limits in place. The reason is simple, it prevents too many players attempting to run the same leve's, side quests and FATES (remember these are generally not instanced) at one time in the same zone. If you've ever been in a really crowded FATE you will understand the problem.
Even if the population spreads out across all zones, there will be hotspots, most probably Uldah, Gridania and Limsa since the guilds, airship and Grand Companies are all there. Vesper Bay will be pretty busy as well because of the Wandering Sands key location. Because the server must reserve enough space for active players to enter these zones during play, there is a concurrent user cap on each zone to prevent over crowding that would affect gameplay. I'd bet we have been running at the cap in a lot of zones on most servers. The concurrent user cap in a zone is smaller than the total server cap since the server cap is made on the assumption of players spreading out.
The net impact is that if you try to login and are in a highly busy zone, you may not get on because the game knows that it cannot add any more users to that zone - even if the total concurrent user base on the server is below 5000. As players spread out, this becomes less problematic, and then we start running into the server concurrent user count problem. If they increase the concurrent user count on the servers and players start spreading out, it will reduce pressure on any one zone, and make getting into the game far, far easier.
An AFK timer would help right now, but may not be needed long term.