Well, if you dutifully clear the fodders and only keep the barest minimum of silvers needed only for your next planned Class Evolution and Awakening, you can go even with just first barracks, but having all three allows one to get away with quite a hoarding) Not to mention keeping silvers and fodders separate tidies the looks of your barracks very well.

And eventually you will want to buy third barracks anyway, if just for a Fairy Barracks devs will introduce behind it. Sure, it is like three years from now, but if you are going to do it anyway, why not now?