I think if they ever introduced a 'mini' stripped down iPhone, they'd do away with selling older iPhone models.
I either envisage a lineup of three previous generations, or the newest and a mini.
I could be wrong though, and I suppose they still sell the iPad 2 alongside the mini and '4'.
The iPhone mini would likely fill the gap of the $0 down with contract, so the lowest tier current iPhone model. Think of it as the equivalent of the iPad Mini.
If we're going by Apple's current selling trends, the iPad 2 is still being sold as the mid-tier iPad, thus I would expect Apple to keep around the previous iPhone also as the mid-tier iPhone, maybe with slight refreshments (iPhone 5.1 or iPhone 5S).
As always, the latest and greatest (iPhone 6) would be the high-end iPhone.
I would anticipate next year Apple will do away with continuing to sell old models, and consistently updating even the low and mid-tier iDevices to remain competitive. Thus, maybe we will see iPhone mini, iPhone, iPhone Pro, designated by a number afterwards to appropriate generations (iPhone mini 1, ect.)
"iPhone 5 Mini"? If more and more people want a bigger screen, wouldn't this go against the general demand?
This mini device would be for emerging markets or consumers that prefer a smaller iOS device. There is demand among women and children too.
Also, Apple isn't the only company doing this. See
THIS