For those replying "Yes, it is called an iPhone" you completely miss the point. You don't call the iPad Mini or iPad or iPad Air or the coming iPad Pro with Cellular data an iPhone do you?
An iPod Touch with Cellular would look a lot like an iPhone, true, but month-to-month, cheaper. I use Verizon, and to add a phone, is $40/mo. To add an iPad is $10/mo. I have younger kids that don't necessarily need a phone, but it would be nice for them to be able to facetime me now and then or send a text, for less than $40/mo. Sure, I could get them a crappy flip-phone (if I can still find one), but they are already used to the iOS interface.
I could also just get a MiFi or something like that, but that is 2 devices to carry, instead of one.
The iPad Mini is nice, but for a kid, still a bit big.
Perhaps Apple could call it the iPad Micro or iPad Nano.