Sure, plot twists can improve the experience a little but a super secret hidden plot twist is kind of gimmicky. A movie like the Sixth Sense is actually harmed by it because the film itself is so good that knowing the secret from the beginning makes the story 100 times more compelling. You're just hiding a big important part of the film. Super secret plot twists are better experienced by the characters than the audience.

When I hear people worried about spoilers, I always think of The Naked Edge. At the end, a title card comes up saying, "Please for the love of god don't tell anyone the plot twist! This movie so fucking boring that the plot twist is all it has!"