WASHINGTON—In the parking lot of the Smithsonian’s smallest museum, 18 of 29 spots were full. But inside, there were no couples on first dates or hordes of tourists milling about the exhibits. In fact, there were no visitors there at all. Just 18 employees waiting for something to do. On a sunny, late-summer day, this reporter stood outside the museum — located in a Washington, D.C., slum, far from any tourists — from noon to 3:00 p.m., ready to count visitors. But there was no one to count. At 12:28 p.m., one woman entered while screaming into her cell phone,...