Not all milongas of the 40s featured live orchestras. There were lots of milongas that played recordings ("baile con grabaciones"). In fact, some of the old milongueros tell us that the more accomplished dancers preferred the dances with recordings. When you went to hear a live orchestra like Di Sarli, Troilo, D'Arienzo, or Pugliese, there could be a few hundred people there (or in some cases, a few thousand) and everyone got up and danced, whether they knew what they were doing or not. So it was often very crowded, the floorcraft could be terrible, and it was sometimes hard to hear the music over the din of the crowd.
Furthermore, as is true today, more accomplished dancers enjoyed dancing to music that they already knew. (Why? That's another discussion.) But the live orchestras were always debuting new material. The "bailes con grabaciones" on the other hand, were often held in social clubs or other small neighborhood establishments, and they often didn't have a lot of discs on hand. In that case they used to play the same song two or three times to make it last longer.
Around 1944, the Odeón recording company mounted a very strong marketing campaign for their tango artists in Argentina. As part of that campaign, they would sponsor certain dances, just like companies today sponsor entertainment or sporting events. They'd subsidize an ad in the newspaper, and provide the discs.
Another advantage of "bailes con grabaciones" was that the entrance fee was a lot lower than for live shows. A dance with a live orchestra could charge two, two-fifty, or three pesos for men (ladies, typically one peso) while a dance with recordings was one peso or less (ladies, fifty centavos or free). That would have made a big difference to a dedicated milonguero on a tight budget who wanted to dance several nights a week!
[Illustrations: El Mundo, 1943, 1944, 1942]