Is Amazon about to send out a free Kindle to each of its millions of Amazon Prime customers? That’s what TechCrunch reporter Michael Arrington said in a post last week, quoting “a reliable source.” Amazon Prime customers, as you probably already know, pay an annual fee of $79 for free two-day (or $3.99 overnight) shipping on all eligible purchases, including all book shipped directly by Amazon.

While there have been some wild claims made in the past about things that Amazon or its competitors might or might not do, this one actually makes a great deal of sense, and Arrington has a stronger track record than most of the gadget press in his Kindle-related reporting. Personally I would find it a little easier to imagine Amazon making a special offer to Amazon Prime customers in which they would deeply discount the Kindle to, say, $99. But then I haven’t spoken to Arrington’s “reliable source.”

It would significantly grow the base of our fellow Kindle owners, provide more of an audience for Kindle Store content, and help Amazon to divert interest from other ebook devices and platforms at the pass. While there would probably be a short-term loss for Amazon in the initial transaction, the company has good reason to be confident that once its loyal Amazon Prime customers try the Kindle they won’t be able to resist buying a lot of Kindle books. One result could be that Amazon’s actual shipping costs for Prime customers could decline as they opt for more ebooks and fewer print editions.

If Arrington’s report is true, and you don’t already have an Amazon Prime account, there’s no time like the present to lay out $79 to get one, especially if it means saving, in effect, at least $180 on that Kindle you have always wanted. (For all the details on Amazon Prime, click here).

How would Amazon handle those current Amazon Prime customers who already own Kindles? Or for that matter, all those Kindle owners who, with or without an Amazon Prime account, have already laid out anywhere from $259 to $489 for a new Kindle? Some early adopters of the Kindle may feel like it is another instance of the old early-adopter tax, but in the long run it is probably also true that the more that Amazon is able to grow its base of Kindle owners, the better it will be for all of us when it comes to pricing and selection for Kindle content.