I think some of it is down to media exposure. It's tempting to think that what you see in a James Bond movie or TV series is a realistic picture of how governments work, without thinking through the practical implications of dispatching "covert action cells" to solve every problem.
There's also been some good research on the psychology of people who are drawn into them.
Why some people are willing to believe conspiracy theories
People can be prone to believe in conspiracy theories due to a combination of personality traits and motivations, including relying strongly on their intuition, feeling a sense of antagonism and superiority toward others, and perceiving threats in their environment, according to research published by the American Psychological Association.
The results of the study paint a nuanced picture of what drives conspiracy theorists, according to lead author Shauna Bowes, a doctoral student in clinical psychology at Emory University.
“Conspiracy theorists are not all likely to be simple-minded, mentally unwell folks—a portrait which is routinely painted in popular culture,” said Bowes. “Instead, many turn to conspiracy theories to fulfill deprived motivational needs and make sense of distress and impairment.”
The researchers also found that people with certain personality traits, such as a sense of antagonism toward others and high levels of paranoia, were more prone to believe conspiracy theories. Those who strongly believed in conspiracy theories were also more likely to be insecure, paranoid, emotionally volatile, impulsive, suspicious, withdrawn, manipulative, egocentric and eccentric.