Those of us who grew up in the Rock and Roll era don't really appreciate what a labor intensive endeavor the Big Band sound was. In both cases, the music found its audience over the radio, but the delivery was completely different.
Rock and Roll has similar roots with Big Band, both coming to us through the "whitening" process of African American Jazz and Blues. Rock was usually the product of a four or five person band who would cut a record and then a disc jockey would play it on a local radio station. Big Band music was performed live over the networks.
Although the Big Bands made "more expensive" music, it was the sound of the OTR era, especially the War years. Rather than the four to five piece combos that formed Rock Bands, a typical Big Band Orchestra would have 17 or more individual players. However, the publicity usually went to the band leader whose name was on the outfit. To a certain extent, the players of the individual instruments were interchangeable; as long as they could play as part of the arrangement and got along with the band leader, they would have a job for as long as the bandleader could get gigs.
The networks had studios which were big enough for a full orchestra to work in, but it was usually easier to take the studio to the band in the form of big band remote broadcasts. All that was needed was an announcer and an engineer to set up in the club or dance hall where the orchestra was working.
Choosing the most important of the Big Bands is a little like asking a class of kindergarten kids to choose their favorite flavor of Jello, there could be a dozen different opinions and all of them would be correct. Names like Tommy and Jimmy Dorsey, Kay Kyser, Artie Shaw, Benny Goodman and Glenn Miller all stand out. It should be remembered that a good many Americans received their first notification about the attack on Pearl Harbor during a broadcast of "Sunday Serenade" with Sammy Kaye over the Blue Network.