Walmart already provides a handful of services of the kind you're mentioning. They have low cost clinic services (at some locations) for flu-shots, eye exams, and prescription drugs. Expanding those services would require having MDs on staff and on location.
There are plenty of businesses trying to offer more accessible medical services also. Urgent Care clinics are becoming popular in New York City, where I live.
None of this is doing much about cost though. The Walmart style sells things cheaply that are allowed to be sold cheaply. They don't sell what they are prevented from selling due to regulations or due to non-viability of offering the service due to staffing limitations. The Urgent Care style is going through the private health insurance system like just about every other medical care provider.
So I suggested an insurance "startup" because the space that seems to lack innovation is the payment side of the health care industry.