For Christmas in 1960, Ron Mei got a Lionel train set. More than 55 years later, he still hasn’t found a better toy.

By creating model railroads, “you learn carpentry,” said Mr. Mei, 62 years old, who runs a motorcycle-parts business in Phoenix and spends 20 to 25 hours a week with his trains. “You learn electric. You learn painting. Kids today, they have skill in one thing—that’s a videogame or a smartphone.”

Once...