They were light and loose fitting, a major change from the much more restricive clothing children wore during the 19th Century Victorian era. Rompers were only worn by younger children and not school-age boys. Time line Rompers first appeared at the turn of the century and were very popular as play wear during the 1920s and early 1930s. They declined in popularity during the 1940s. Rompers have continued to be worn even after the 1920s and 1930s as play wear.
Usage appears to have varried somewhat between Europe and America.
European boys, especially Itlalian and perhaps French boys continued to wear rompers into the 1950s. Euroean boys continued to wear rompers into the 1950s for both play and casual wear and dressy outfits. They were often worn with white socks and strap shoes. I know Italian boys wore them and French boys might have also wore them. I'm not sure about the age deemed apporopriate, but I would think they were worn much as American boys wore shortalls in the 1960s.