The reasons why the Fire is a great machine are few and simple.
It's a conduit for Amazon Prime—it jacks straight into a huge, rich library of media, and allows you to buy, read, listen to, or watch it with great ease. The Fire is a simple plastic and rubber cup—but it's filled with rich liquor. Everything else—apps, email, messaging, maps, photography—is either secondary or nonexistent. The Fire's purpose is crystalline.
It also sports a build of Android so far removed from its kin that it's near unrecognisable. Which is great, because Android is typically everything that pleasure reading is not; cold, unfriendly, alienating. The Fire's interface is inviting, familiar, and fun. The bookshelf UI is almost perfect.
And, finally, it's nice to hold. Maybe it could be an inch bigger! Sure. But as it is, the Fire feels good in your hands, regardless of what kind of stuff you're stimulating your brain with. It's a great screen for nice things to look at.
A Kindle phone would pretty much kick all of these lovely qualities down a gulch.
A smartphone, by definition, needs to be way more than the Fire defines itself as. It needs to make and take calls, send messages, kill email, snap terrific photos, and guide you around town. It needs to be a multifaceted, a program prism, where the Fire is deliberately myopic—focused on giving you things to comfortably enjoy.
Amazon could easily plug a phone into Prime, of course—it's just a matter of software. But would we want it? How often do we stream movies on our phones, as opposed to tablets, computers, or televisions? When was the last time you read an entire book on your smartphone? The mini screen is great for YouTube or personal video, but are you going to watch a film on your phone unless you're stuck on four hour bus ride and that's your only diversion?
To achieve any of this on a phone, most importantly Amazon would have to gut its interface—the shelf would be shattered. The Fire's minimalist UI just wouldn't translate to a phone's small screen—you couldn't read anything. It'd be a nightmare. So it'd have to make their Android device seem more like an Android device, which would be a regrettable regression, and one less reason to care. What excitement is there in yet another Android phone in a flaming lake of them, even if it carries Kindle branding and Prime access? Without the shelf metaphor, the Fire would be just another tablet, and a Kindle phone would be just another handset.
So please, Amazon—stick with what you've done well. Nobody thought you could pull off a real tablet, but you did with aplomb. But don't get cocky. You'll screw it all up. People might buy the Fire because it says KINDLE on it, but they'll enjoy it because of the design. I doubt we'll be able to say the same about a phone.