Michael Douglas is detailing just how much streaming has affected the role of producers in Hollywood. The actor/producer, who at Cannes was celebrating the 50th anniversary of “One Flew Over the Cuckoo’s Nest,” which he produced and won an Oscar for, told Deadline that Silicon Valley-based companies such as Amazon and Apple have “inhaled Hollywood.” And that’s even despite filmmaking not being their core conglomerate purpose.

“Today, streaming has taken over. It has inhaled Hollywood. It’s very lucrative,” Douglas said. “Silicon Valley made us look like paupers. For Amazon and Apple, movies are a side business. At the same time, many of the great screenwriters went to work in TV and streaming.”

Douglas, who won the Best Picture Oscar alongside Saul Zaentz for “Cuckoo’s Nest,” recalled how the iconic Miloš Forman film itself fared in theaters. The drama made history as one of the three films...