Paperless shopping, please: Receipts mailed to your inbox?

It occurred to me recently that while my local grocery shop has all my details thanks to their persistence in getting me to sign up for their bonus card, they still force-feed me paper receipts of my purchases every single time. This might be for legal reasons (proof of purchase, etc.), but I would say the time has come to offer a smarter alternative via the magical, new-fangled system called e-mail.

Imagine you are in the self-check-out lane, finishing up your purchase, and instead of having the blaring machine implore you to grab the multiple bits of paper (receipt, coupons, customer copy of the receipt), you're given the choice of sending it to your e-mail address. The e-mail would include the UUID of your purchase, and links to CSV/PDF files of your purchase, plus coupons and other marketing garbage. As an added service, at the end of the month you would receive a tally e-mail of all your purchases, also with CSV/PDF versions downloadable from a secure site.

Why has no store chain implemented this yet? They'd save money on paper purchases, it would speed up the check-out process, and they have a reason to send me an e-mail that they can fill up with marketing stuff!