For anyone curious about how this might play out, take a look at Telus Health. Telus is a Canadian telecom company that has branched out into several health care businesses, from clinics to building and hosting¹ electronic healthcare records. There are currently battles over whether it is legal to force prescription fulfillment through Telus providers.
That's right, a telecom company, that most reviled, least trusted sector of the economy, is trying to take over healthcare in a country with a (mostly) single-payer, tax-funded, (mostly) free at the point of delivery, public healthcare system. And they're doing so successfully.
Amazon is actually late to the game.
(1) I don't know for sure that they are hosting the records, but the fact that the word "Telus" shows up in the url makes it seem like like a reasonable conclusion.