I think a story without secrets can be interesting, but it will never hook the reader.. it won't ever elicit that *gasp* that we, as writers, should be trying to draw from our audience. A secret, given time to be set up and develop naturally, that is then revealed, can be all the difference between, "It was a good story." and "I've GOT to get the next book she writes!"
An example.. imagine Luke Skywalker, sitting in Obi Wan Kanobi's dirt igloo abode on Tatooine, looking at an old light saber and asking Obi Wan about the Force.. only to be told, "Oh yeah, and your Dad, well he made some bad life decisions and.. well he goes by Darth Vader these days."
Interesting twist, no? Luke's dad is the black clad uber villain in the Universe.. cool.
Now.. imagine Luke learning that Vader had killed his father, he spends months training to meet Vader to get retribution, he grows in power and maturity.. he's finally ready to face the man who killed his father and exact his revenge. Then, in the moment when Luke is at his most vulnerable, when it appears he's lost.. even the world he knows is stripped away by one simple secret revealed.
Having the ability to reveal a secret gives you the power to do literally anything you like. You can change a character from bad to good, or vice versa, you can reveal a characters true nature and motivations, and you can completely change the direction of your story midstream.
Look at Luke.. he went from a young naive boy full of reckless bravado to, once he went through the process of dealing with the sudden revelation, a wisened adult confident and capable.
One of the most powerful *gasp* moments of all time.. all because of a secret that was revealed at the right time.
How could I forget the biggest *gasp* moment of recent literature.. when we learn the truth about Severus Snape in the Harry Potter series. Again, HUGE secret.. expertly held by JK Rowling until just the right time to discover the true nature of Snape, and of his bargain with Dumbledore, even the one at the very end.. (Trying not to put a spoiler in there just in case someone in the world actually hasn't read the Harry Potter Books.. or seen the movies as well I suppose, although how you could only see the movies and not read the books is beyond me.)