Alex Ruiz, 29 years old, and his wife, Stephanie Johnson, have steady jobs, are setting aside money for retirement and are slowly paying down their student debt.

Yet buying a house seems out of reach for at least another decade. Home values in Asheville, N.C., where they live, are up some 70% over the past seven years. Their student-loan payments and rising rent have made it difficult to save for a down payment, and the houses that go on the market get snapped up right away.

“Day...