I dont think that is the only thing they'll have. Cuz soon an iphone 6 will come out...
The reason its keeping AT&T cuz they were the 1st and only for years. Once verizon got it, deff harmed att
AT&T was exclusive for 5 years and IMHO that's a significant factor in getting them to where they are today. If Sprint had the iPhone 5 exclusively for even six months, I think it would do them a lot of good. Three months (of less) of exclusivity, not so much.
Another thing is, if there are supply constraints in the beginning, can't Sprint use that as an excuse for not fulfilling their commitment to Apple? (parenthetically, methinks the whole 'supply constraint' thing was artificially orchestrated by Apple to increase the hype (and keep their inventories lean)).