Technically this already exists. There's Amazon Subscribe & Save (and similar) for this reason, pretty much. It may not be a subscription like you are describing, but it accomplishes the goal: set it and forget it for consistent grocery (or other) purchases, and get a nice discount.

I wonder if a legit subscription service, for perhaps a select group of items that a user consistently purchases, would work. Could be complicated when things like eggs fluctuate so much in price.