More likely, they would do what Netflix is doing when faced with the same problem (time-limited licenses): they would commission more original music from cheaper, less-known (and likely younger) artists.
Honestly, I can survive the thought of not having a Bowie song in every other production.
I don't know about Hollywood movies, but for TV shows that would require the makers buying a perpetual license for anything they use in the show. That would probably make it too expensive to make something anyone would actually want to watch. Shows would have to have no cultural references (eg a pop song) in them at all.