It is unreasonable to expect that any secret that is published will be kept a secret for any length of time. It is true that people had been remarkably good-natured about keeping the plot-twist of the Mousetrap to themselves. But had they gone the other way, Agatha Christie would have no grounds to complain. That is the nature of the beast: a secret that is told, is no longer a secret. I don't see why this would impact the arts. After all, people still read Shakespear even after knowing that Macbeth turns evil (yes - sue me), and read "The wizard of Oz" even after knowing that the Wizard is an old man from Omaha (again - sue me), and watch Friends reruns on TV even after knowing that Rachel and Ross get together in the end (once again - sue me). People still go to see the Mona Lisa, climb the Eiffel, visit the Sistine Chapel, even though they know full well what they will see. In most of the arts, its the journey that matters - not the punch line at the end.
I do appreciate that some stories are fully about the plot twist. To take an example from Christie's work - nobody can forget who the murderer is, once they know who killed Roger Ackroyd. But publishing a work of art does not give one a license to muzzle one's audience. So, while Agatha Christie (and her descendants) may politely request people to refrain from spoiling details, they should shut up when people excercise their freedom of expression.