The 1920's was a time of great cultural advancement in many different areas, especially in the arts. Many technologies were beginning to become mainstream all across the country such as electricity, automobiles, and telephones. The decade is also known as the "Roaring Twenties" as it was a time of great economic prosperity with increased consumer spending and great strides in GDP (graph linked below). It makes even more sense in my mind that these period is romanticized because it goes directly in contrast with the following decade which is arguably one of the worst economic decades in United States history with the Great Depression. The twenties would be considered a Boom in the economic cycle link sourced below, obviously, the next decade the United States quickly fell into a depression.

Sources:

1. YouTube Video Explaining the Twenties (A very good, simple explanation)

• GDP of the United States between the 1920's and the 1940's
• Economic Cycle of a Capitalist Economy

Some things to consider:

Prohibition created a lot of folk heroes and villains. The battle with organized crime makes a great setting for dramatic fiction. The FBI (then the BOI) was still in its infancy and Hoover was trying to secure its role in American society with his war on crime.

Early electric lighting, and specifically the relatively new phenomenon of electric signage, gave the period a unique, counter intuitively dark feel. Night life developed as a concept during this period, and as a result "night" as a principal setting for fiction also developed. Directors of 40s and 50s films and television immortalized this imagery in American culture in film noir works. Check out "The Age of Edison: Electric Light and the Invention of Modern America" for more on this. Electric lights combined with art deco aesthetics gave the period a unique visual quality that resonates with many people today.

The aforementioned development of a night life was tied into the creation of large amounts of uniquely American culture like swing dancing and jazz.

You also need to look at the cultures that popularized the 20s for your answer, not just the 20s themselves. Perhaps later generations of men wistfully idealized an age where they believe men were masculine, sharp dressed, and commanding. The series "Mad Men" is set in the 60s but it owes much of its popularity to the same tropes as commonly ascribed to the 1920s.

This is less of an answer and more of a group of suggestions for areas for further research. It's a broad and subjective question so it's the best I can do for you really.