Ok. I may have this figured out. You pay the full price for the PAPER book and then you get a special gift card good only for the purchase of the e-book version (which is not transferable and sellable, so would not be prone to abuse or lower the market rate of the printed book)
Even if Amazon were receptive to the idea, agency pricing takes most ebook pricing completely out of Amazon hands (including discounts and coupons). The publishers would have to give it their blessing—and why would they?
In short, Amazon doesn't have the authority to give away (or deep discount) the publishers ebooks, regardless of how you dress it up. The publisher sets the ebook price period.
It might work with publishers other than the Big Six, but that's about it.
Plus Amazon would never survive, they'd basically be giving away free (or cheap) pbooks and still paying the publishers full retail for the ebook you "bought" with their gift card (plus whatever they owe the publisher for the pbook). Why would they want to lose cash on every transaction like that?