GERTE AND SEAMOUR Shavin of Chattanooga, Tennessee, were sure the legendary Frank Lloyd Wright would be too busy to design a house for them. So they wrote a letter, in 1949, asking him to recommend a good architect. Wright responded, “The best one I know is myself,” Gerte, now 95, recalls.

In 1954, Bette Koprivica Pappas, now 90, and her husband, Theodore (since deceased), spent a week composing a missive to Wright, asking him to design a house for them outside St. Louis. They expressed both trepidation (“I don’t know if...