Why trad jazz? Because there was a revival - just as there is now a hard bop/Blue Note revival. (Check Smalls jazz club on YouTube).
As for the traditional jazz revival, look into Kid Ory, Bunk Johnson, George Lewis and Ken Colyer.
The Barber band in the videos must now be seen as something of a classic (I saw them once in 1957), a legitimate offshoot and development from the New Orleans jazz of an earlier era. (Listening to 1950s Bechet, Lyttelton and Barber soon took me to Morton, Oliver and Armstrong.)