Especially when server capacity is such an obvious issue. Having people spamming log in attempts while a good portion of players logged in did so before going to work or whatever is kind of rough. Yes, it is comparatively few perhaps, but you have a Queue feature limited to a couple hundred long, and nothing in place to prevent people staying in the game for hours at a time while they are AFK. It seems like solving this would be easy to apply, and in the very least, have the people in the game playing the game. This would at least justify those banging their heads against the door to get in as there would be a higher turnover rate.
Cities have pay parking for a similar reason, to increase turnover and the number of people "served".
This games primary hurdle at the moment is that the demand far outstrips the ability to supply, something still probably after the approaching server increases. You have stopped selling digital copies of the game to boot. Does it not make sense to additionally enforce some level of proper use of your servers? What so far is being taught to players is that you need to log in early in the day, or waste copious amounts of time spamming the log in screen to have a chance at playing the game. The people waiting at the doors are mostly people who would be actively playing, let them in, kick the afk's out. It benefits the majority by enabling more people to enjoy their purchase actively, which helps Square.
The game is great, and I am sure things will get better soon. It just seems to me this is a viable quick fix using something that is quite common within the genre already. Later if you wish you could always remove the function, but for now it seems entirely warranted. Also, dramatically increasing the server queue would in the least save a larger number of people the need to buttonmash the 0 button.
Thanks for your time.