You can NOT play the whole of the game with just one character.

To play the WHOLE of the game you need at least three.
I like the story in this game but as a citizen of Ul'dah and member of the maelstrom I had no idea what the other cities and grand companies stories were like, so I made 2 more character because we are locked into those choices. Maybe in 2.0 that will change, but what good does that do me now seeing as the story is going to be drastically different in 2.0.

Also, some times I get bored of being a Miqo'te and want to see something from the perspective of a lalafell.

And when I'm out of anima and leve allowance but still want to play and feel like I'm accomplishing something it is nice to have an alt to play with...

There are plenty of reasons to have multiple characters in this game just like in XI and the additional cost per slot does not feel to me adequately justified by "I can be multiple class" when at the same time I am locked into key aspects of the game in the same fashion that other games lock you into one class but you can still experience all of the content.