In a battle over the future of U.S. health care, a question emerges: Is primary care scalable?

The J.P. Morgan Healthcare Conference is a place for the well-heeled to get a readout on the next six-figure cancer drug, or learn about the gene-altering technology promising to defang a debilitating disease and send stock prices soaring.

But at this year’s conference, investors also entertained pitches from a part of the industry known more for its enduring economic problems than its profit potential: the humble primary care practice.