So far, that hasn't happened. But the former head of Amazon Prime, Rob Schwietzer, who was in charge of scaling the product to millions of people, is now working in health care. He left Amazon in 2013, and for the past year, he's been leading product at 98point6, a Seattle-based start-up that is looking to build the next consumer health brand.
"Health care is really hard," Schwietzer told CNBC. "But I do believe that people shouldn't have to make decisions about whether they should go see a doctor when they need one, or go buy groceries for their family."
Schwietzer has teamed up with CEO Robbie Cape, a Microsoft veteran who created Cozi, a family planning software venture, then sold it to Time. Back in 2011, Cape contacted Schweitzer out of the blue to get some advice on subscription businesses, as Prime was one of the few services millions of people were willing to pay for every month.
To his surprise, Schwietzer responded and the pair had lunch.
Years later, when Cape had the idea for 98point6, he reached out to his old friend Schwietzer. He had his misgivings about health care after a stint in consulting early in his career, but Schwietzer said he saw a big opportunity to bring "price, quality, and convenience" to the sector, similarly to what Amazon did for retail.
"Why I think Amazon does so well," Schwietzer explained, "is that where most companies will look at something and say 'we'll give it to you fast or inexpensive,' Amazon has always said 'why not both?'"
Meaningful innovation in health care could not only create a huge business -- health care spending has now reached $3.5 trillion -- but also make a meaningful difference. Studies have shown that improving access to high-quality family doctors can help drive down health care costs and improve patient's health outcomes, but not everyone can afford it or reliably access it.
That's because there's a shortage of primary care physicians and nurses in the U.S., which is only getting more pronounced with the aging population. People in rural areas are often hours away from the nearest clinic, and many will forgo care until they end up in the emergency room.
Cape and Schwietzer are not the first entrepreneurs to hone in on this problem.
A movement called direct primary care involves charging consumers a subscription fee for access to high-quality doctors, mostly in person. Direct primary care makes up less than ten percent of physician practices, but the Trump administration is now asking how it could help fund some of these practices for vulnerable seniors on Medicare.
Other start-ups are trying to increase access to primary care by experimenting with virtual-only approaches, such as smartphone apps to connect doctors and patients, like Doctor on Demand or AmericanWell. In general, insurance pays for these services, or they charge patients a fee of $40 to $50 per visit.
But 98point6 believes it's onto something different by blending these two worlds, and leveraging technology to bring down the price. It now offers a messaging service for patients and doctors to connect at an introductory price of $20 a year with no additional fees for a visit (after the first year, it costs $120).
The subscription model can also help patient health by supporting an ongoing relationship between doctor and patient, Cape believes. "Our hope is that will engage with our users literally every month about something related to their health," he said.
Apart from the price tag, the big draw for consumers is the ability to message a doctor at any time. As more consumers start to use it, that will cut down on the administrative work that is "burning out" doctors, potentially turning them into advocates for the product.
One example is the 98point6 assistant, essentially a bot, that conducts about half of the initial interview with the patient and presents that information to the doctor (Cape expects that percentage to increase over time, as the technology gets smarter).
98point6 is also pushing to get companies to cover the service.
The company told CNBC that about 50 self-insured employers have signed up so far, ranging from Seattle Children's Hospital to Washington-based Red Lion Hotels. Cape said that the utilization rate for their service, meaning the percentage of employees who take advantage of the benefit, is higher than most at about 6 percent (the average for telemedicine hovers around 2 or 3 percent for a number of reasons, including a lack of awareness among employees).
As a result, growth is starting to take off. The company said it now has 160,000 members, either enrolled through their employer or paying for it out-of-pocket. As of January, it's licensed to practice medicine in all 50 states plus Washington, D.C.
Cape recruited another Amazon cloud vet, Damon Lanphear, to run the technology team. It has also hired 16 doctors, including a chief medical officer who still practices, Brad Younggren. A former Surgeon General under the Obama administration, Regina Benjamin, now sits on its board.
Investors seem to agree that there's big potential in the idea. 98point6 recently raised $50 million from Goldman Sachs' merchant banking division, with the rest flowing in from individual investors including BlackRock CEO Larry Fink, Costco founder and former CEO Jim Sinegal, former Goldman Sachs CFO David Viniar, and Frazier Healthcare Partners' managing partner Nader Naini.
"There are younger generations of people who don't want to spend their time going to the doctor but are so comfortable using technology," said Viniar, who currently serves on the board of both Goldman Sachs and 98point6. "And there are people in this country who live far from the doctor's office, or can't afford it," he continued.
Outsiders note that 98point6 will face ample competition as it looks to grow from existing players in the digital health space, as well as potential new rivals like the major pharmacy chains that are dabbling in health care services and the largest technology giants. Both Amazon and Apple are building out medical clinics for their own employees, which suggests a willingness to get into the business of actually delivering care.
"It'll be a clash of titans," said Michael Yang, a veteran health-technology investor and a managing partner with OMERS Ventures. But 98point6 has a good shot, Yang said, if what it ultimately comes down to is "your starting point, your talent and your runway to get there."
But 98point6 is optimistic, is hoping to scale it to millions of people, on par with a household name brand like Amazon Prime.
"Everyone claims to have a great value proposition," said Cape. "But that needs to be combined that an experience that people literally want to talk about. An experience that is so good that you just want to tell people about it."