I'm sure some reastaurants were cooking brisket before the depression but it and WWII were big drivers. Edgar Black, Jr. said that when he started cooking BBQ for his Dad after WWII there weren't as many as half a dozen other BBQ places in Texas serving it.
Also, the book Republic of Barbecue - Stories beyond the Brisket has some interviews from old time TX BBQ cooks where they discuss brisket.
For example, Vencil Mares is quoted as stating that back in the 1940's "Them days, they didn't hardly ever cook briskets. They didn't know what to do with them. I remember when they was thirty-nine cents and people didn't even want them."
Bobby Mueller said that he couldn't get boneless briskets until the 1960s.
So, economics and supply capability did play a big part in popularizing brisket.
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